ICSE Class 7 Mathematics · Selina Solutions Concise Mathematics Class 7 ICSE · 72 solved questions
Find the gain or loss percent, if:
C.P. = ₹ 200 and S.P. = ₹ 224
C.P. = ₹ 200 and S.P. = ₹ 224
Since S.P. > C.P., there is a gain.
Gain = S.P. − C.P. = 224 − 200 = ₹ 24.
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{24}{200} \times 100\right)$%
= $\frac{2,400}{200}$%
= 12%
Hence, the gain percent is 12%.
Find the gain or loss percent, if:
C.P. = ₹ 450 and S.P. = ₹ 400
C.P. = ₹ 450 and S.P. = ₹ 400
Since C.P. > S.P., there is a loss.
Loss = C.P. − S.P. = 450 − 400 = ₹ 50.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{50}{450} \times 100\right)$%
= $\frac{5,000}{450}$%
= $\frac{100}{9}$%
= $11\frac{1}{9}$%
Hence, the loss percent is $11\frac{1}{9}$%.
Find the gain or loss percent, if:
C.P. = ₹ 550 and gain = ₹ 22
C.P. = ₹ 550 and gain = ₹ 22
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{22}{550} \times 100\right)$%
= $\frac{2,200}{550}$%
= 4%
Hence, the gain percent is 4%.
Find the gain or loss percent, if:
C.P. = ₹ 216 and loss = ₹ 72
C.P. = ₹ 216 and loss = ₹ 72
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{72}{216} \times 100\right)$%
= $\frac{7,200}{216}$%
= $\frac{100}{3}$%
= $33\frac{1}{3}$%
Hence, the loss percent is $33\frac{1}{3}$%.
Find the gain or loss percent, if:
S.P. = ₹ 500 and loss = ₹ 100
S.P. = ₹ 500 and loss = ₹ 100
C.P. = S.P. + loss = 500 + 100 = ₹ 600.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{100}{600} \times 100\right)$%
= $\frac{10,000}{600}$%
= $\frac{50}{3}$%
= $16\frac{2}{3}$%
Hence, the loss percent is $16\frac{2}{3}$%.
Find the selling price, if:
C.P. = ₹ 500 and gain = 25%
C.P. = ₹ 500 and gain = 25%
S.P. = C.P. $\times \left(1 + \frac{\text{gain percentage}}{100}\right)$
$$\begin{aligned}= 500 \times \left(1 + \frac{25}{100}\right)\\[1em] = 500 \times \frac{125}{100}\\[1em] = ₹\ 625\end{aligned}$$
Hence, the selling price of the article is ₹ 625.
Find the selling price, if:
C.P. = ₹ 60 and loss = $12\frac{1}{2}$%
C.P. = ₹ 60 and loss = $12\frac{1}{2}$%
As, $12\frac{1}{2}$% $= \frac{25}{2}$%
S.P. = C.P. $\times \left(1 - \frac{\text{loss percentage}}{100}\right)$
$$\begin{aligned}= 60 \times \left(1 - \frac{25}{200}\right)\\[1em] = 60 \times \frac{175}{200}\\[1em] = ₹\ 52.50\end{aligned}$$
Hence, the selling price of the article is ₹ 52.50.
Rohit bought a tape recorder for ₹ 1,500 and sold it for ₹ 1,800. Calculate his profit or loss percent.
C.P. = ₹ 1,500 and S.P. = ₹ 1,800.
Since S.P. > C.P., there is a profit.
Profit = 1,800 − 1,500 = ₹ 300.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{300}{1,500} \times 100\right)$%
= $\frac{30,000}{1,500}$%
= 20%
Hence, Rohit made a profit of 20%.
An article bought for ₹ 350 is sold at a profit of 20%. Find its selling price.
C.P. = ₹ 350 and profit = 20%.
S.P. = C.P. $\times \left(1 + \frac{\text{profit percentage}}{100}\right)$
$$\begin{aligned}= 350 \times \frac{120}{100}\\[1em] = \frac{42,000}{100}\\[1em] = ₹\ 420\end{aligned}$$
Hence, the selling price of the article is ₹ 420.
An old machine is bought for ₹ 1,400 and is sold at a loss of 15%. Find its selling price.
C.P. = ₹ 1,400 and loss = 15%.
S.P. = C.P. $\times \left(1 - \frac{\text{loss percentage}}{100}\right)$
$$\begin{aligned}= 1,400 \times \frac{85}{100}\\[1em] = \frac{1,19,000}{100}\\[1em] = ₹\ 1,190\end{aligned}$$
Hence, the selling price of the machine is ₹ 1,190.
Oranges are bought at 5 for ₹ 10 and sold at 6 for ₹ 15. Find profit or loss as percent.
C.P. of 1 orange = $\frac{10}{5}$ = ₹ 2.
S.P. of 1 orange = $\frac{15}{6}$ = ₹ 2.50.
Since S.P. > C.P., there is a profit.
Profit on 1 orange = 2.50 − 2 = ₹ 0.50.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{0.50}{2} \times 100\right)$%
= $\frac{50}{2}$%
= 25%
Hence, the profit percent is 25%.
A certain number of articles are bought at 3 for ₹ 150 and all of them are sold at 4 for ₹ 180. Find the loss or gain as percent.
C.P. of 1 article = $\frac{150}{3}$ = ₹ 50.
S.P. of 1 article = $\frac{180}{4}$ = ₹ 45.
Since C.P. > S.P., there is a loss.
Loss on 1 article = 50 − 45 = ₹ 5.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{5}{50} \times 100\right)$%
= $\frac{500}{50}$%
= 10%
Hence, the loss percent is 10%.
A vendor bought 120 sweets at 20 p each. In his house, 18 were consumed and he sold the remaining at 30 p each. Find his profit or loss as percent.
Total C.P. = 120 × 20 p = 2,400 p = ₹ 24.
Number of sweets sold = 120 − 18 = 102.
Total S.P. = 102 × 30 p = 3,060 p = ₹ 30.60.
Since S.P. > C.P., there is a profit.
Profit = 30.60 − 24 = ₹ 6.60.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{6.60}{24} \times 100\right)$%
= $\frac{660}{24}$%
= 27.5%
Hence, the profit percent is 27.5%.
The cost price of an article is ₹ 1,200 and selling price is $\frac{5}{4}$ times of its cost price. Find:
(i) selling price of the article,
(ii) profit or loss as percent.
C.P. = ₹ 1,200 and S.P. = $\frac{5}{4}$ times of C.P.
(i) S.P. = $\frac{5}{4} \times 1,200$
= $\frac{6,000}{4}$
= ₹ 1,500
Hence, the selling price of the article is ₹ 1,500.
(ii) Since S.P. > C.P., there is a profit.
Profit = 1,500 − 1,200 = ₹ 300.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{300}{1,200} \times 100\right)$%
= $\frac{30,000}{1,200}$%
= 25%
Hence, the profit percent is 25%.
The selling price of an article is ₹ 1,200 and cost price is $\frac{5}{4}$ times of its selling price. Find:
(i) cost price of the article,
(ii) profit or loss as percent.
S.P. = ₹ 1,200 and C.P. = $\frac{5}{4}$ times of S.P.
(i) C.P. = $\frac{5}{4} \times 1,200$
= $\frac{6,000}{4}$
= ₹ 1,500
Hence, the cost price of the article is ₹ 1,500.
(ii) Since C.P. > S.P., there is a loss.
Loss = 1,500 − 1,200 = ₹ 300.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{300}{1,500} \times 100\right)$%
= $\frac{30,000}{1,500}$%
= 20%
Hence, the loss percent is 20%.
Find the cost price, if:
S.P. = ₹ 21 and gain = 5%
S.P. = ₹ 21 and gain = 5%
C.P. = $\frac{\text{S.P.} \times 100}{100 + \text{gain percentage}}$
$$\begin{aligned}= \frac{21 \times 100}{100 + 5}\\[1em] = \frac{2,100}{105}\\[1em] = ₹\ 20\end{aligned}$$
Hence, the cost price of the article is ₹ 20.
Find the cost price, if:
S.P. = ₹ 22 and loss = 12%
S.P. = ₹ 22 and loss = 12%
C.P. = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
$$\begin{aligned}= \frac{22 \times 100}{100 - 12}\\[1em] = \frac{2,200}{88}\\[1em] = ₹\ 25\end{aligned}$$
Hence, the cost price of the article is ₹ 25.
Find the cost price, if:
S.P. = ₹ 340 and gain = ₹ 20
S.P. = ₹ 340 and gain = ₹ 20
C.P. = S.P. − gain
= 340 − 20
= ₹ 320
Hence, the cost price of the article is ₹ 320.
Find the cost price, if:
S.P. = ₹ 200 and loss = ₹ 50
S.P. = ₹ 200 and loss = ₹ 50
C.P. = S.P. + loss
= 200 + 50
= ₹ 250
Hence, the cost price of the article is ₹ 250.
Find the cost price, if:
S.P. = ₹ 1 and loss = 5 p
S.P. = ₹ 1 = 100 p and loss = 5 p
C.P. = S.P. + loss
= 100 + 5
= 105 p
= ₹ $\frac{105}{100}$
= ₹ 1.05
Hence, the cost price of the article is ₹ 1.05.
By selling an article for ₹ 810, a loss of 10 percent is suffered. Find its cost price.
S.P. = ₹ 810 and loss = 10%.
C.P. = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
$$\begin{aligned}= \frac{810 \times 100}{100 - 10}\\[1em] = \frac{81,000}{90}\\[1em] = ₹\ 900\end{aligned}$$
Hence, the cost price of the article is ₹ 900.
By selling a scooter for ₹ 9,200, a man gains 15%. Find the cost price of the scooter.
S.P. = ₹ 9,200 and gain = 15%.
C.P. = $\frac{\text{S.P.} \times 100}{100 + \text{gain percentage}}$
$$\begin{aligned}= \frac{9,200 \times 100}{100 + 15}\\[1em] = \frac{9,20,000}{115}\\[1em] = ₹\ 8,000\end{aligned}$$
Hence, the cost price of the scooter is ₹ 8,000.
On selling an article for ₹ 2,640, a profit of 10 percent is made. Find:
(i) cost price of the article.
(ii) new selling price of it, in order to gain 15%.
S.P. = ₹ 2,640 and profit = 10%.
(i) C.P. = $\frac{\text{S.P.} \times 100}{100 + \text{profit percentage}}$
$$\begin{aligned}= \frac{2,640 \times 100}{110}\\[1em] = \frac{2,64,000}{110}\\[1em] = ₹\ 2,400\end{aligned}$$
Hence, the cost price of the article is ₹ 2,400.
(ii) New S.P. = C.P. $\times \frac{100 + 15}{100}$
$$\begin{aligned}= 2,400 \times \frac{115}{100}\\[1em] = \frac{2,76,000}{100}\\[1em] = ₹\ 2,760\end{aligned}$$
Hence, the new selling price of the article is ₹ 2,760.
A T.V. set is sold for ₹ 6,800 at a loss of 15%. Find:
(i) cost price of the T.V. set.
(ii) new selling price of it, in order to gain 12%.
S.P. = ₹ 6,800 and loss = 15%.
(i) C.P. = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
$$\begin{aligned}= \frac{6,800 \times 100}{85}\\[1em] = \frac{6,80,000}{85}\\[1em] = ₹\ 8,000\end{aligned}$$
Hence, the cost price of the T.V. set is ₹ 8,000.
(ii) New S.P. = C.P. $\times \frac{100 + 12}{100}$
$$\begin{aligned}= 8,000 \times \frac{112}{100}\\[1em] = \frac{8,96,000}{100}\\[1em] = ₹\ 8,960\end{aligned}$$
Hence, the new selling price of the T.V. set is ₹ 8,960.
A fruit seller bought mangoes at ₹ 90 per dozen and sold them at a loss of 8 percent. How much will a customer pay for:
(i) one mango
(ii) 40 mangoes
C.P. of 1 dozen (12) mangoes = ₹ 90 and loss = 8%.
S.P. of 12 mangoes = C.P. $\times \frac{100 - 8}{100}$
$$\begin{aligned}= 90 \times \frac{92}{100}\\[1em] = \frac{8,280}{100}\\[1em] = ₹\ 82.80\end{aligned}$$
So, the S.P. of 12 mangoes = ₹ 82.80.
(i) S.P. of 1 mango = $\frac{\text{S.P. of 12 mangoes}}{12} = \frac{82.80}{12}$ = ₹ 6.90.
Hence, a customer will pay ₹ 6.90 for one mango.
(ii) S.P. of 40 mangoes = 40 × 6.90 = ₹ 276.
Hence, a customer will pay ₹ 276 for 40 mangoes.
By selling two transistors for ₹ 600 each, a shopkeeper gains 20 percent on one transistor and loses 20 percent on the other. Find:
(i) C.P. of each transistor.
(ii) total C.P. and total S.P. of both the transistors.
(iii) profit or loss percent on the whole.
(i) For the first transistor (gain 20%), S.P. = ₹ 600.
C.P. of first = $\frac{\text{S.P.} \times 100}{100 + \text{gain percentage}}$
= $\frac{600 \times 100}{100 + 20}$
= $\frac{60,000}{120}$
= ₹ 500
For the second transistor (loss 20%), S.P. = ₹ 600.
C.P. of second = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
= $\frac{600 \times 100}{100 - 20}$
= $\frac{60,000}{80}$
= ₹ 750
Hence, the cost prices of the two transistors are ₹ 500 and ₹ 750 respectively.
(ii) Total C.P. = 500 + 750 = ₹ 1,250.
Total S.P. = 600 + 600 = ₹ 1,200.
Hence, the total cost price is ₹ 1,250 and the total selling price is ₹ 1,200.
(iii) Since total C.P. > total S.P., there is a loss.
Loss = 1,250 − 1,200 = ₹ 50.
Loss% = $\left(\frac{\text{loss}}{\text{total C.P.}} \times 100\right)$%
= $\left(\frac{50}{1,250} \times 100\right)$%
= $\frac{5,000}{1,250}$%
= 4%
Hence, the loss percent on the whole is 4%.
Mangoes are bought at 20 for ₹ 60. If they are sold at a profit of $33\frac{1}{3}$ percent, find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
C.P. of 1 mango = $\frac{60}{20}$ = ₹ 3 and profit = $33\frac{1}{3}$% $= \frac{100}{3}$%.
(i) S.P. of 1 mango = C.P. $\times \left(1 + \frac{\text{profit percentage}}{100}\right)$
$$\begin{aligned}= 3 \times \left(1 + \frac{100}{3 \times 100}\right)\\[1em] = 3 \times \left(1 + \frac{1}{3}\right)\\[1em] = 3 \times \frac{4}{3}\\[1em] = ₹\ 4\end{aligned}$$
Hence, the selling price of each mango is ₹ 4.
(ii) S.P. of 8 mangoes = 8 × 4 = ₹ 32.
Hence, the selling price of 8 mangoes is ₹ 32.
Find the cost price of an article, which is sold for ₹ 4,050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
S.P. = ₹ 4,050 and loss = 10%.
C.P. = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
$$\begin{aligned}= \frac{4,050 \times 100}{90}\\[1em] = \frac{4,05,000}{90}\\[1em] = ₹\ 4,500\end{aligned}$$
Hence, the cost price of the article is ₹ 4,500.
New S.P. = C.P. $\times \frac{100 + 8}{100}$
$$\begin{aligned}= 4,500 \times \frac{108}{100}\\[1em] = \frac{4,86,000}{100}\\[1em] = ₹\ 4,860\end{aligned}$$
Hence, the new selling price of the article is ₹ 4,860.
By selling an article for ₹ 825, a man loses an amount equal to $\frac{1}{3}$ of its selling price. Find:
(i) the cost price of the article.
(ii) the profit percent or the loss percent made, if the same article is sold for ₹ 1,265.
S.P. = ₹ 825.
(i) Loss = $\frac{1}{3}$ of S.P. = $\frac{1}{3} \times 825$ = ₹ 275.
C.P. = S.P. + loss = 825 + 275 = ₹ 1,100.
Hence, the cost price of the article is ₹ 1,100.
(ii) When the article is sold for ₹ 1,265:
Since S.P. > C.P., there is a profit.
Profit = 1,265 − 1,100 = ₹ 165.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{165}{1,100} \times 100\right)$%
= $\frac{16,500}{1,100}$%
= 15%
Hence, the profit percent made is 15%.
Find the loss or gain as percent, if the C.P. of 10 articles, all of the same kind, is equal to S.P. of 8 articles.
Let the C.P. of each article be ₹ x.
C.P. of 10 articles = ₹ 10x.
Given, C.P. of 10 articles = S.P. of 8 articles.
So, S.P. of 8 articles = ₹ 10x.
S.P. of 1 article = $\frac{10x}{8}$ = ₹ $\frac{5x}{4}$.
Since S.P. > C.P., there is a gain.
Gain on 1 article = $\frac{5x}{4} - x$ = ₹ $\frac{x}{4}$.
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{\frac{x}{4}}{x} \times 100\right)$%
= $\left(\frac{1}{4} \times 100\right)$%
= 25%
Hence, the gain percent is 25%.
Find the loss or gain as percent, if the C.P. of 8 articles, all of the same kind, is equal to S.P. of 10 articles.
Let the C.P. of each article be ₹ x.
C.P. of 8 articles = ₹ 8x.
Given, C.P. of 8 articles = S.P. of 10 articles.
So, S.P. of 10 articles = ₹ 8x.
S.P. of 1 article = $\frac{8x}{10}$ = ₹ $\frac{4x}{5}$.
Since C.P. > S.P., there is a loss.
Loss on 1 article = $x - \frac{4x}{5}$ = ₹ $\frac{x}{5}$.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{x/5}{x} \times 100\right)$%
= $\left(\frac{1}{5} \times 100\right)$%
= 20%
Hence, the loss percent is 20%.
The cost price of an article is 96% of its selling price. Find the loss or the gain as percent on the whole.
Let the S.P. of the article be ₹ 100.
C.P. = 96% of S.P. = $\frac{96}{100} \times 100$ = ₹ 96.
Since S.P. > C.P., there is a gain.
Gain = 100 − 96 = ₹ 4.
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{4}{96} \times 100\right)$%
= $\frac{400}{96}$%
= $\frac{25}{6}$%
= $4\frac{1}{6}$%
Hence, the gain percent is $4\frac{1}{6}$%.
The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Let the C.P. of the article be ₹ 100.
S.P. = 96% of C.P. = $\frac{96}{100} \times 100$ = ₹ 96.
Since C.P. > S.P., there is a loss.
Loss = 100 − 96 = ₹ 4.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{4}{100} \times 100\right)$%
= 4%
Hence, the loss percent is 4%.
Hundred oranges are bought for ₹ 350 and all of them are sold at the rate of ₹ 48 per dozen. Find the profit percent or loss percent made.
C.P. of 100 oranges = ₹ 350.
S.P. of 1 orange = $\frac{48}{12}$ = ₹ 4.
S.P. of 100 oranges = 100 × 4 = ₹ 400.
Since S.P. > C.P., there is a profit.
Profit = 400 − 350 = ₹ 50.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{50}{350} \times 100\right)$%
= $\frac{5,000}{350}$%
= $\frac{100}{7}$%
= $14\frac{2}{7}$%
Hence, the profit percent is $14\frac{2}{7}$%.
Oranges are bought at 100 for ₹ 80 and all of them are sold at 80 for ₹ 100. Find the loss or gain as percent in this transaction.
Let the number of oranges be 100.
C.P. of 100 oranges = ₹ 80.
S.P. of 1 orange = $\frac{100}{80}$ = ₹ 1.25.
S.P. of 100 oranges = 100 × 1.25 = ₹ 125.
Since S.P. > C.P., there is a gain.
Gain = 125 − 80 = ₹ 45.
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{45}{80} \times 100\right)$%
= $\frac{4,500}{80}$%
= $\frac{225}{4}$%
= 56.25%
Hence, the gain percent is 56.25%.
An article is bought for ₹ 5,700 and ₹ 1,300 is spent on its repairing, transportation, etc. For how much should this article be sold in order to gain 20% on the whole?
Total C.P. = cost + expenses = 5,700 + 1,300 = ₹ 7,000.
Gain = 20%.
S.P. = C.P. $\times \frac{100 + 20}{100}$
$$\begin{aligned}= 7,000 \times \frac{120}{100}\\[1em] = \frac{8,40,000}{100}\\[1em] = ₹\ 8,400\end{aligned}$$
Hence, the article should be sold for ₹ 8,400 in order to gain 20% on the whole.
Rani bought an old machine for ₹ 4,800 and spent ₹ 1,200 on its repairs. If she sold the repaired machine for ₹ 5,400, find her profit or loss, as percent, on this transaction.
Total C.P. = cost + repairs = 4,800 + 1,200 = ₹ 6,000.
S.P. = ₹ 5,400.
Since C.P. > S.P., there is a loss.
Loss = 6,000 − 5,400 = ₹ 600.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{600}{6,000} \times 100\right)$%
= $\frac{60,000}{6,000}$%
= 10%
Hence, Rani made a loss of 10%.
A machine is marked at ₹ 5,000 and is sold at a discount of 10%. Find the selling price of the machine.
Marked price = ₹ 5,000 and discount = 10%.
S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}= 5,000 \times \frac{90}{100}\\[1em] = \frac{4,50,000}{100}\\[1em] = ₹\ 4,500\end{aligned}$$
Hence, the selling price of the machine is ₹ 4,500.
A shopkeeper marked a dinner set for ₹ 1,000. He sold it at ₹ 900. What percent discount did he give?
Marked price = ₹ 1,000 and S.P. = ₹ 900.
Discount = M.P. − S.P. = 1,000 − 900 = ₹ 100.
Discount% = $\left(\frac{\text{discount}}{\text{M.P.}} \times 100\right)$%
= $\left(\frac{100}{1,000} \times 100\right)$%
= $\frac{10,000}{1,000}$%
= 10%
Hence, the shopkeeper gave a discount of 10%.
A pair of shoes, marked at ₹ 320, are sold at a discount of 15 percent. Find:
(i) the discount,
(ii) the selling price of the shoes.
Marked price = ₹ 320 and discount = 15%.
(i) Discount = $\frac{\text{discount percentage}}{100} \times$ M.P.
= $\frac{15}{100} \times 320$
= $\frac{4,800}{100}$
= ₹ 48
Hence, the discount is ₹ 48.
(ii) S.P. = M.P. − discount = 320 − 48 = ₹ 272.
Hence, the selling price of the shoes is ₹ 272.
The list price of an article is ₹ 450 and it is sold for ₹ 360. Find:
(i) the discount,
(ii) the discount percent.
List (marked) price = ₹ 450 and S.P. = ₹ 360.
(i) Discount = M.P. − S.P. = 450 − 360 = ₹ 90.
Hence, the discount is ₹ 90.
(ii) Discount% = $\left(\frac{\text{discount}}{\text{M.P.}} \times 100\right)$%
= $\left(\frac{90}{450} \times 100\right)$%
= $\frac{9,000}{450}$%
= 20%
Hence, the discount percent is 20%.
A shopkeeper buys an article for ₹ 300. He increases its price by 20% and then gives 10% discount on the new price. Find:
(i) the new price (marked price) of the article.
(ii) the discount given by the shopkeeper.
(iii) the selling price.
(iv) the profit percent made by the shopkeeper.
C.P. = ₹ 300.
(i) Marked price = C.P. increased by 20% = $300 \times \frac{120}{100}$
= $\frac{36,000}{100}$
= ₹ 360
Hence, the marked price of the article is ₹ 360.
(ii) Discount = 10% of 360 = $\frac{10}{100} \times 360$ = ₹ 36.
Hence, the discount given by the shopkeeper is ₹ 36.
(iii) S.P. = M.P. − discount = 360 − 36 = ₹ 324.
Hence, the selling price of the article is ₹ 324.
(iv) Since S.P. > C.P., there is a profit.
Profit = 324 − 300 = ₹ 24.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{24}{300} \times 100\right)$%
= $\frac{2,400}{300}$%
= 8%
Hence, the profit percent made by the shopkeeper is 8%.
A car is marked at ₹ 50,000. The dealer gives 5% discount on first ₹ 20,000 and 2% discount on the remaining ₹ 30,000. Find:
(i) the total discount.
(ii) the price charged by the dealer.
Marked price = ₹ 50,000.
(i) Discount on first ₹ 20,000 = 5% of 20,000 = $\frac{5}{100} \times 20,000$ = ₹ 1,000.
Discount on remaining ₹ 30,000 = 2% of 30,000 = $\frac{2}{100} \times 30,000$ = ₹ 600.
Total discount = 1,000 + 600 = ₹ 1,600.
Hence, the total discount is ₹ 1,600.
(ii) Price charged = M.P. − total discount = 50,000 − 1,600 = ₹ 48,400.
Hence, the price charged by the dealer is ₹ 48,400.
A dealer buys a T.V. set for ₹ 2,500. He marks it at ₹ 3,200 and then gives a discount of 10% on it. Find:
(i) the selling price of the T.V. set
(ii) the profit percent made by the dealer.
C.P. = ₹ 2,500 and marked price = ₹ 3,200.
(i) S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}= 3,200 \times \left(1 - \frac{10}{100}\right)\\[1em] = 3,200 \times \frac{90}{100}\\[1em] = \frac{2,88,000}{100}\\[1em] = ₹\ 2,880\end{aligned}$$
Hence, the selling price of the T.V. set is ₹ 2,880.
(ii) Since S.P. > C.P., there is a profit.
Profit = 2,880 − 2,500 = ₹ 380.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{380}{2,500} \times 100\right)$%
= $\frac{38,000}{2,500}$%
= 15.2%
Hence, the profit percent made by the dealer is 15.2%.
A sells his goods at 15% discount. Find the marked price of an article which is sold for ₹ 680.
S.P. = ₹ 680 and discount = 15%.
S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}\Rightarrow 680 = \text{M.P.} \times \left(1 - \frac{15}{100}\right)\\[1em] \Rightarrow 680 = \text{M.P.} \times \frac{85}{100}\\[1em] \Rightarrow \text{M.P.} = \frac{680 \times 100}{85}\\[1em] \Rightarrow \text{M.P.} = ₹\ 800\end{aligned}$$
Hence, the marked price of the article is ₹ 800.
A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges ₹ 560.
S.P. = ₹ 560 and discount = 20%.
S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}\Rightarrow 560 = \text{M.P.} \times \left(1 - \frac{20}{100}\right)\\[1em] \Rightarrow 560 = \text{M.P.} \times \frac{80}{100}\\[1em] \Rightarrow \text{M.P.} = \frac{560 \times 100}{80}\\[1em] \Rightarrow \text{M.P.} = ₹\ 700\end{aligned}$$
Hence, the marked price of the article is ₹ 700.
An article is bought for ₹ 1,200 and ₹ 100 is spent on its transportation, etc. Find:
(i) the total C.P. of the article.
(ii) the selling price of it in order to gain 20% on the whole.
(i) Total C.P. = cost + transportation = 1,200 + 100 = ₹ 1,300.
Hence, the total cost price of the article is ₹ 1,300.
(ii) Gain = 20%.
S.P. = C.P. $\times \frac{100 + 20}{100}$
$$\begin{aligned}= 1,300 \times \frac{120}{100}\\[1em] = \frac{1,56,000}{100}\\[1em] = ₹\ 1,560\end{aligned}$$
Hence, the selling price of the article is ₹ 1,560.
40 pens are bought at 4 for ₹ 50 and all of them are sold at 5 for ₹ 80. Find:
(i) C.P. of one pen.
(ii) S.P. of one pen.
(iii) Profit made by selling one pen.
(iv) Profit percent made by selling one pen.
(v) C.P. of 40 pens.
(vi) S.P. of 40 pens.
(vii) Profit made by selling 40 pens.
(viii) Profit percent made by selling 40 pens.
Are the results of parts (iv) and (viii) same?
What conclusion do you draw from the above result?
(i) C.P. of one pen = $\frac{50}{4}$ = ₹ 12.50.
Hence, the C.P. of one pen is ₹ 12.50.
(ii) S.P. of one pen = $\frac{80}{5}$ = ₹ 16.
Hence, the S.P. of one pen is ₹ 16.
(iii) Profit on one pen = 16 − 12.50 = ₹ 3.50.
Hence, the profit made by selling one pen is ₹ 3.50.
(iv) Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{3.50}{12.50} \times 100\right)$%
= $\frac{350}{12.50}$%
= 28%
Hence, the profit percent made by selling one pen is 28%.
(v) C.P. of 40 pens = 40 × 12.50 = ₹ 500.
Hence, the C.P. of 40 pens is ₹ 500.
(vi) S.P. of 40 pens = 40 × 16 = ₹ 640.
Hence, the S.P. of 40 pens is ₹ 640.
(vii) Profit on 40 pens = 640 − 500 = ₹ 140.
Hence, the profit made by selling 40 pens is ₹ 140.
(viii) Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{140}{500} \times 100\right)$%
= $\frac{14,000}{500}$%
= 28%
Hence, the profit percent made by selling 40 pens is 28%.
Yes, the results of parts (iv) and (viii) are the same, i.e. 28%.
Hence, the profit percent does not depend on the number of articles bought and sold; it remains the same whether it is calculated for one pen, 40 pens or 100 pens.
The C.P. of 5 identical articles is equal to S.P. of 4 articles. Calculate the profit percent or loss percent made if all the articles bought have been sold.
Let the C.P. of each article be ₹ x.
C.P. of 5 articles = ₹ 5x.
Given, C.P. of 5 articles = S.P. of 4 articles.
So, S.P. of 4 articles = ₹ 5x.
S.P. of 1 article = $\frac{5x}{4}$.
Since S.P. > C.P., there is a profit.
Profit on 1 article = $\frac{5x}{4} - x$ = ₹ $\frac{x}{4}$.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{x/4}{x} \times 100\right)$%
= $\left(\frac{1}{4} \times 100\right)$%
= 25%
Hence, the profit percent is 25%.
The C.P. of 12 pens is the same as the S.P. of 15 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold.
Let the C.P. of each pen be ₹ x.
C.P. of 12 pens = ₹ 12x.
Given, C.P. of 12 pens = S.P. of 15 pens.
So, S.P. of 15 pens = ₹ 12x.
S.P. of 1 pen = $\frac{12x}{15}$ = ₹ $\frac{4x}{5}$.
Since C.P. > S.P., there is a loss.
Loss on 1 pen = $x - \frac{4x}{5}$ = ₹ $\frac{x}{5}$.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{x/5}{x} \times 100\right)$%
= $\left(\frac{1}{5} \times 100\right)$%
= 20%
Hence, the loss percent is 20%.
A certain number of articles are bought at ₹ 450 per dozen and all of them are sold at a profit of 20%. Find the S.P. of:
(i) one article
(ii) seven articles.
C.P. of 1 dozen (12) articles = ₹ 450.
C.P. of 1 article = $\frac{450}{12}$ = ₹ 37.50 and profit = 20%.
(i) S.P. of 1 article = C.P. $\times \frac{100 + 20}{100}$
$$\begin{aligned}= 37.50 \times \frac{120}{100}\\[1em] = \frac{4,500}{100}\\[1em] = ₹\ 45\end{aligned}$$
Hence, the selling price of one article is ₹ 45.
(ii) S.P. of 7 articles = 7 × 45 = ₹ 315.
Hence, the selling price of seven articles is ₹ 315.
An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Let the C.P. of the article be ₹ 100.
Marked price = C.P. increased by 60% = $100 \times \frac{160}{100}$ = ₹ 160.
S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}= 160 \times \left(1 - \frac{20}{100}\right)\\[1em] = 160 \times \frac{80}{100}\\[1em] = \frac{12,800}{100}\\[1em] = ₹\ 128\end{aligned}$$
Since S.P. > C.P., there is a profit.
Profit = 128 − 100 = ₹ 28.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{28}{100} \times 100\right)$%
= 28%
Hence, the profit percent is 28%.
An old bicycle is bought for ₹ 675 and ₹ 125 is spent on its repairs. If the repaired bicycle is sold for ₹ 880, the profit or loss as percent is:
Total C.P. = 675 + 125 = ₹ 800.
S.P. = ₹ 880.
Since S.P. > C.P., there is a profit.
Profit = 880 − 800 = ₹ 80.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{80}{800} \times 100\right)$%
= $\frac{8,000}{800}$%
= 10%
Hence, option 1 is the correct option.
The cost price of 20 pens is equal to the selling price of 16 pens; the profit or loss as percent is:
Let the C.P. of each pen be ₹ x.
C.P. of 20 pens = ₹ 20x = S.P. of 16 pens.
S.P. of 1 pen = $\frac{20x}{16}$ = ₹ $\frac{5x}{4}$.
Since S.P. > C.P., there is a profit.
Profit on 1 pen = $\frac{5x}{4} - x$ = ₹ $\frac{x}{4}$.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{x/4}{x} \times 100\right)$%
= 25%
Hence, option 4 is the correct option.
The C.P. of 16 pens is equal to the S.P. of 20 pens; the profit or loss as percent is:
Let the C.P. of each pen be ₹ x.
C.P. of 16 pens = ₹ 16x = S.P. of 20 pens.
S.P. of 1 pen = $\frac{16x}{20} = ₹ \frac{4x}{5}$.
Since C.P. > S.P., there is a loss.
Loss on 1 pen = $x - \frac{4x}{5} = ₹ \frac{x}{5}$.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{\frac{x}{5}}{x} \times 100\right)$%
= 20%
Hence, option 1 is the correct option.
An article is bought for ₹ 15,000 and ₹ 1,000 is spent on its repairs. If the article is sold at 20% profit, the selling price is:
Total C.P. = 15,000 + 1,000 = ₹ 16,000.
S.P. = C.P. $\times \frac{100 + 20}{100}$
$$\begin{aligned}= 16,000 \times \frac{120}{100}\\[1em] = \frac{19,20,000}{100}\\[1em] = ₹\ 19,200\end{aligned}$$
Hence, option 4 is the correct option.
Rasheed buys a certain number of bananas at 2 for ₹ 1 and sold all of them at ₹ 1 each. The profit or loss made is:
C.P. of 1 banana = $\frac{1}{2}$ = ₹ 0.50.
S.P. of 1 banana = ₹ 1.
Since S.P. > C.P., there is a profit.
Profit = 1 − 0.50 = ₹ 0.50.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{0.50}{0.50} \times 100\right)$%
= 100%
Hence, option 1 is the correct option.
Two identical articles are bought at ₹ 300 each. If one is sold at 25% profit and the other at 25% loss. The profit or loss made on the whole is:
Total C.P. = 300 + 300 = ₹ 600.
S.P. of first (25% profit) = $300 \times \frac{125}{100}$ = ₹ 375.
S.P. of second (25% loss) = $300 \times \frac{75}{100}$ = ₹ 225.
Total S.P. = 375 + 225 = ₹ 600.
Since total S.P. = total C.P., there is neither profit nor loss.
Hence, option 2 is the correct option.
Two articles are sold for ₹ 300 each. If on one article, a profit of 25% is made and on the other a loss of 25% is made. The profit or the loss made on the whole is:
S.P. of each article = ₹ 300.
C.P. of first (25% profit) = $\frac{\text{S.P.} \times 100}{100 + \text{profit percentage}}$
= $\frac{300 \times 100}{125}$
= ₹ 240
C.P. of second (25% loss) = $\frac{\text{S.P.} \times 100}{100 - \text{loss percentage}}$
= $\frac{300 \times 100}{75}$
= ₹ 400
Total C.P. = 240 + 400 = ₹ 640.
Total S.P. = 300 + 300 = ₹ 600.
Since C.P. > S.P., loss = 640 − 600 = ₹ 40.
Hence, option 2 is the correct option.
Mohit purchased an article for ₹ 1,000 and sold for ₹ 3,000. The profit percent made is:
C.P. = ₹ 1,000 and S.P. = ₹ 3,000.
Profit = 3,000 − 1,000 = ₹ 2,000.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{2,000}{1,000} \times 100\right)$%
= 200%
Hence, option 3 is the correct option.
The S.P. of an article is $\frac{4}{5}$ of its C.P. The profit or loss as percent is:
Let the C.P. be ₹ 5.
S.P. = $\frac{4}{5}$ of 5 = ₹ 4.
Since C.P. > S.P., there is a loss.
Loss = 5 − 4 = ₹ 1.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{1}{5} \times 100\right)$%
= 20%
Hence, option 1 is the correct option.
The C.P. of an article is $\frac{4}{5}$ of its S.P. The profit or loss as percent is:
Let the S.P. be ₹ 5.
C.P. = $\frac{4}{5}$ of 5 = ₹ 4.
Since S.P. > C.P., there is a profit.
Profit = 5 − 4 = ₹ 1.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{1}{4} \times 100\right)$%
= 25%
Hence, option 4 is the correct option.
The marked price of a T.V. is ₹ 60,000 which is available at a discount of 25%. For this T.V., a customer will pay:
Marked price = ₹ 60,000 and discount = 25%.
S.P. = M.P. $\times \left(1 - \frac{\text{discount percentage}}{100}\right)$
$$\begin{aligned}= 60,000 \times \left(1 - \frac{25}{100}\right)\\[1em] = 60,000 \times \frac{75}{100}\\[1em] = \frac{45,00,000}{100}\\[1em] = ₹\ 45,000\end{aligned}$$
Hence, option 2 is the correct option.
A calculator is marked at ₹ 600 and is available at a discount of ₹ 100. If on selling, a profit of ₹ 100 is made, its cost price is:
Marked price = ₹ 600 and discount = ₹ 100.
S.P. = M.P. − discount = 600 − 100 = ₹ 500.
C.P. = S.P. − profit = 500 − 100 = ₹ 400.
Hence, option 2 is the correct option.
The single discount equivalent to two successive discounts of 20% and 20% is:
Let the marked price be ₹ 100.
After the first discount of 20%: price = 100 − 20 = ₹ 80.
After the second discount of 20% on ₹ 80: price = 80 − $\frac{20}{100} \times 80$ = 80 − 16 = ₹ 64.
Total discount = 100 − 64 = ₹ 36.
So, the single equivalent discount = 36%.
Hence, option 2 is the correct option.
By selling an article for ₹ 800, a loss of ₹ 200 is made. The loss percent is:
S.P. = ₹ 800 and loss = ₹ 200.
C.P. = S.P. + loss = 800 + 200 = ₹ 1,000.
Loss% = $\left(\frac{\text{loss}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{200}{1,000} \times 100\right)$%
= 20%
Hence, option 1 is the correct option.
By selling an article for ₹ 800, a gain of ₹ 200 is made. The gain percent is:
S.P. = ₹ 800 and gain = ₹ 200.
C.P. = S.P. − gain = 800 − 200 = ₹ 600.
Gain% = $\left(\frac{\text{gain}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{200}{600} \times 100\right)$%
= $\frac{20,000}{600}$%
= $\frac{100}{3}$%
= $33\frac{1}{3}$%
Hence, option 3 is the correct option.
Statement 1: Discount is always given on the cost price.
Statement 2: S.P. = Marked price × $\left(1 + \frac{d}{100}\right)$, where d is discount %.
Which of the following options is correct?
We know that,
Discount is always given on the marked price of an article, not on the cost price.
So, Statement 1 is false.
Since discount is subtracted from the marked price, the correct relation is S.P. = Marked price × $\left(1 - \frac{d}{100}\right)$, where d is the discount %.
So, Statement 2 is false.
Hence, option 2 is the correct option.
Assertion (A): Ajay sold his laptop for ₹ 25,000 at a profit of ₹ 2,250. Ajay's profit % is 9%.
Reason (R): Profit % = $\left(\frac{\text{Profit}}{\text{C.P.}} \times 100\right)$%
S.P. = ₹ 25,000 and profit = ₹ 2,250.
C.P. = S.P. − profit = 25,000 − 2,250 = ₹ 22,750.
Profit% = $\left(\frac{\text{profit}}{\text{C.P.}} \times 100\right)$%
= $\left(\frac{2,250}{22,750} \times 100\right)$%
= $\frac{900}{91}$%
= 9.89% (approx.), which is not 9%.
So, Assertion (A) is false.
Profit % = $\left(\frac{\text{Profit}}{\text{C.P.}} \times 100\right)$% is the correct formula.
So, Reason (R) is true.
Hence, option 2 is the correct option.
Assertion (A): A bicycle marked at ₹ 12,500 is sold for ₹ 10,500. Discount offered by the shopkeeper is 16%.
Reason (R): Discount % = $\left(\frac{\text{Discount}}{\text{C.P.}} \times 100\right)$%
Marked price = ₹ 12,500 and S.P. = ₹ 10,500.
Discount = M.P. − S.P. = 12,500 − 10,500 = ₹ 2,000.
Discount% = $\left(\frac{\text{discount}}{\text{M.P.}} \times 100\right)$%
= $\left(\frac{2,000}{12,500} \times 100\right)$%
= 16%
So, Assertion (A) is true.
Discount % is calculated on the marked price, not on the C.P. The correct formula is Discount % = $\left(\frac{\text{Discount}}{\text{M.P.}} \times 100\right)$%.
So, Reason (R) is false.
Hence, option 1 is the correct option.
Assertion (A): A shopkeeper buys 100 bicycles at ₹ 1,000 each. He spends ₹ 1,000 on transportation and paid ₹ 400 on road tax. He sells all the bicycles at ₹ 1,050 each. Thus he is making a profit of ₹ 3,000.
Reason (R): If an article is purchased for some amount and there are some additional expenses on transportation, labour, tax, etc., then these expenses are added to get the total cost price.
Total C.P. = (100 × 1,000) + 1,000 + 400 = 1,00,000 + 1,400 = ₹ 1,01,400.
Total S.P. = 100 × 1,050 = ₹ 1,05,000.
Profit = 1,05,000 − 1,01,400 = ₹ 3,600, which is not ₹ 3,000.
So, Assertion (A) is false.
If an article is purchased for some amount and there are some additional expenses on transportation, labour, tax, etc., then these expenses are added to the purchase price to get the total cost price. This is correct.
So, Reason (R) is true.
Hence, option 2 is the correct option.
Assertion (A): The price of a jacket was ₹ 960 in the month of December. The same jacket is available in off season at ₹ 816. Off season discount % is 15%.
Reason (R): Marked price (M.P.) is the price that is printed on the article.
Marked price = ₹ 960 and off-season price = ₹ 816.
Discount = 960 − 816 = ₹ 144.
Discount% = $\left(\frac{\text{discount}}{\text{M.P.}} \times 100\right)$%
= $\left(\frac{144}{960} \times 100\right)$%
= 15%
So, Assertion (A) is true.
Marked price (M.P.) is the price that is printed on the article. This is correct.
So, Reason (R) is true.
Hence, option 3 is the correct option.
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