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MATHS [3 marks sum]

Profit, Loss and Discount · ICSE STD 7 (ICSE - English Medium). 22 questions.

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22 questions · timed · auto-graded

Question 13 Marks
A shopkeeper allows 20% discount on the marked price of his articles. Find the marked price of an article for which he charges Rs. 560.
Answer
Let Marked price (M.P.) = Rs. 100
Discount $=20 \%$
$\therefore$ S.P. of that article $=$ Rs. $100-20=$ Rs. 80
If S.P. is Rs. 80, then marked price $=$ Rs. 100
and if S.P. is Rs. 560, then marked price
$ =\text { Rs. } \frac{100 \times 560}{80}=\text { Rs. } 700 $
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Question 23 Marks
A sells his goods at 15% discount. Find the price of an article which is sold for Rs. 680.
Answer
S.P. of an article $=$ Rs. 680
Rate of discount $=15 \%$
Let M.P. of the article = Rs. 100
$\therefore$ S.P. $=$ Rs. $100-15=$ Rs. 85
If S.P. is Rs. 85, then M.P. = Rs. 100
and if S.P. is Rs. 680, then M.P.
$ =\text { Rs. } \frac{100 \times 680}{85}=\text { Rs. } 800 $
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Question 33 Marks
A car is marked at Rs. 50,000. The dealer gives 5% discount on first Rs. 20,000 and 2% discount on the remaining Rs. 30,000. Find:
(i) the total discount.
(ii) the price charged by the dealer.
Answer
Marked price (M.P.) of a car = Rs. 50000
Discount at the rate of $5 \%$ on first
Rs. $20000=$ Rs. $\frac{20000 \times 5}{100}=$ Rs. 1000
Discount at the rate of $2 \%$ on remaining
$ \text { Rs. } 30000=\text { Rs. } \frac{30000 \times 2}{100}=\text { Rs. } 600 $
(i) $\therefore$ Total discount $=$ Rs. $1000+$ Rs. 600
$ =\text { Rs. } 1600 $
(ii) Price charged by the dealer
$ =\text { Rs. } 50000 \text { - Rs. } 1600 \text { = Rs. } 48400 $
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Question 43 Marks
The list price of an article is ₹450 and it is sold for ₹360. Find: (i) discount (ii) discount percent
Answer
360
(i). Amount of discount = M.P. - S.P
= ₹ 450 - ₹ 360 = ₹ 90
(ii) Discount percent = $\frac{\text { Discount } \times 100}{\text { M.P. }}$
$=\frac{90 \times 100}{450}=20 \%$
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Question 53 Marks
A pair of shoes marked at ₹320 are sold at a discount of 15 percent. Find: (i) discount (ii) selling price of the shoes.
Answer
Marked Price (M.P.) of shoes = ₹ 320
Rate of discount = 15%
(i).. Amount of discount = ₹ $\frac{320 \times 15}{100}=$ ₹ 48
(ii) Selling price = M.P. - Discount
= ₹ 320 - 48 = ₹ 272
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Question 63 Marks
The shopkeeper marked a dinner set for ₹1000. He sold it at ₹900, what percent discount did he give?
Answer
Marked price of a dinner set = ₹ 1000
and selling price (S.P.) = ₹ 900
$\therefore$ Amount of discount = Rs. 1000 - Rs. 900 = ₹ 100
$\therefore$ Discount percent = $\frac{\text { Discount } \times 100}{\text { M.P. }}$
$=\frac{100 \times 100}{1000}=10 \%$
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Question 73 Marks
A certain number of articles are bought at Rs. 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.
Answer
C.P. of 1 dozen articles $=$ Rs. 450
Profit $=20 \%$
$ \begin{aligned} & \therefore \text { S.P. }=\frac{\text { C.P. } \times(100+\text { Profit })}{100} \\ & =\text { Rs. } \frac{450 \times(100+20)}{100} \\ & =\text { Rs. } \frac{450 \times 120}{100}=\text { Rs. } 540 \end{aligned} $
(i) $\therefore$ S.P. of 1 article $=$ Rs. $\frac{540}{12}=$ Rs. 45
(ii) S.P. of 7 articles $=$ Rs. $45 \times 7=$ Rs. 315
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Question 83 Marks
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 are sold.
Answer
C.P. of 5 articles $=$ S.P. of 4 articles
Let C.P. of 5 articles $=$ S.P. of 4 articles $=$ Rs. 100
$\therefore$ C.P. of 1 articles $=$ Rs. $\frac{100}{5}=$ Rs. 20
and S.P. of 1 article $=$ Rs. $\frac{100}{4}=$ Rs. 25
$\therefore$ Profit $=$ S.P. - C.P. $=$ Rs. $25-$ Rs.. $20=$ Rs. 5
$\therefore$ Profit $\%=\frac{\text { Profit } \times 100}{\text { C.P. }}=\frac{5 \times 100}{20}=25 \%$
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Question 93 Marks
A machine is marked at ₹5000 and is sold at a discount of 10%. Find the selling price of the machine.
Answer
Marked price (M.P.) of the machine = ₹ 5000
Rate of discount = 10%
... Amount of discount = ₹ 5000 × $\frac{10}{100}$  = ₹ 500
.. Selling price = M.P. discount
= ₹ 5000 - ₹ 500 = ₹ 4500
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Question 103 Marks
Mangoes are bought at 20 for Rs. 60. If they are sold at 33 percent profit. Find:
(i) selling price of each mango.
(ii) S.P. of 8 mangoes.
Answer
C.P. of 20 mangoes $=$ Rs. 60
$ \begin{aligned} & \text { Gain }=33 \frac{1}{3} \%=\frac{100}{3} \% \\ & \therefore \text { S.P. of } 20 \text { mangoes }=\frac{\text { C.P. } \times(100+\text { gain } \%)}{100} \\ & =\frac{60\left(100+\frac{100}{3}\right)}{100} \\ & =\text { Rs. } \frac{60 \times 400}{100 \times 3}=\text { Rs. } 80 \end{aligned} $
(i) S.P. of 1 mango $=$ Rs. $\frac{80}{20}=$ Rs. 4
(ii) S.P. of 8 mangoes $=$ Rs. $4 \times 8=$ Rs. 32
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Question 113 Marks
A fruit seller bought mangoes at Rs. 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
Answer
C.P. of 1 dozen or 12 mangoes $=$ Rs. 90
$ \text { Loss }=8 \% $
$\therefore$ S.P. of 1 dozen or 12 mangoes
$ \begin{aligned} & =\frac{\text { C.P. } \times(100-\operatorname{loss} \%)}{100} \\ & =\text { Rs. } \frac{90(100-8)}{100}=\frac{90 \times 92}{100}=\frac{828}{10}=\text { Rs. } 82.80 \end{aligned} $
(i) S.P. of 1 mango $=\frac{82.80}{12}=$ Rs. 6.90
(ii) S.P. of 40 mangoes $=$ Rs. $6.90 \times 40=$ Rs. 276
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Question 123 Marks
By selling an article for Rs. 810, a loss of 10 percent is suffered. Find its cost price.
Answer
S.P. of an article $=$ Rs. 810
$ \text { Loss }=10 \% $
$ \therefore \text { C.P. }=\frac{\text { S.P. } \times 100}{100-\operatorname{Loss} \%} $
$ \begin{aligned} & =\frac{810 \times 100}{100-10} \\ & =\frac{810 \times 100}{90} \end{aligned} $
Rs. 900
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Question 133 Marks
The cost price of an article is $96\%$ of its selling price. Find the loss or the gain as percent on the whole.
Answer
Let S.P $= ₹ 100$
C.P. $96\%$ of S.P.
$= ₹ \frac{96}{100} \times 100= ₹ 96$
$\therefore$ Gain $=₹ 100 - ₹ 96 = ₹ 4$
and, gain percent
$=\frac{\text { Gain } \times 100}{\text { C.P. }}$
$=\frac{4}{96} \times 100 \%$
$=\frac{25}{6} \text { or } 4 \frac{1}{6} \%$
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Question 143 Marks
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.
Answer
C.P. of $8$ articles $=$ S.P. of $10$ articles $= ₹ 80$ (suppose)
$\therefore$ C.P. of $1$ article $=\frac{80}{8}= ₹ 10$
and S.P. of $1$ article $=\frac{80}{10}=  ₹ 8$
$\therefore$ Loss $=$ C.P - S.P $= ₹ 10 - ₹ 8 = ₹ 2$
$\text { Loss } \%=\frac{\text { Loss } \times 100}{\text { C.P. }}$
$=\frac{2 \times 100}{10}=20 \%$
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Question 153 Marks
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.
Answer
C.P. of $10$ articles = S.P. of $8$ articles ₹ 80 (Suppose)
$\therefore$ C.P. of 1 article $=\frac{80}{10}=$ ₹ $8$
and S.P. of $1$ article $=\frac{80}{8}=$ ₹ 10
$\therefore$ Gain $=$ S.P. - C.P. $= ₹ 10 - ₹ 8 = ₹ 2$
$\text { Gain } \%=\frac{\text { Gain } \times 100}{\text { C.P. }}$
$=\frac{2 \times 100}{8}=25 \%$
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Question 163 Marks
An old machine is bought for Rs. 1,400 and is sold at a loss of 15%. Find its selling price.
Answer

$\begin{aligned} & \text { C.P. of the machine }=\text { Rs. } 1400 \\ & \text { Loss }=15 \% \\ & \therefore \text { S.P. }=\frac{\text { C.P }(100-\text { Loss } \%)}{100} \\ & =\frac{1400(100-15)}{100} \\ & =\text { Rs. } \frac{1400 \times 85}{100} \\ & =\text { Rs. } 1190\end{aligned}$
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Question 173 Marks
An article bought for Rs. 350 is sold at a profit of 20%. Find its selling price.
Answer

$\begin{aligned} & \text { C.P. of article }=\text { Rs. } 350 \\ & \text { Profit }=20 \% \\ & \therefore \text { S.P. }=\frac{\text { C.P. }(100+\text { Profit } \%)}{100} \\ & =\text { Rs. } \frac{350(100+20)}{100} \\ & =\text { Rs. } \frac{350 \times 120}{100} \\ & =\text { Rs. } 420\end{aligned}$
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Question 183 Marks
Rohit bought a tape-recorder for Rs. 1,500 and sold it for Rs. 1,800. Calculate his profit or loss percent.
Answer

$\begin{aligned} & \text { C.P. of tape-recorder }=\text { Rs. } 1500 \\ & \text { S.P. }=\text { Rs. } 1800 \\ & \therefore \text { Gain }=\text { S.P. }- \text { C.P. } \\ & =\text { Rs. } 1800-\text { Rs. } 1500=\text { Rs. } 300 \\ & \text { Gain } \%=\frac{\text { Gain } \times 100}{\text { C.P. }} \\ & =\frac{300 \times 100}{1500}=20 \%\end{aligned}$
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Question 193 Marks
Find the selling price, if: C.P. = Rs. 80 and gain = 2.5%
Answer
C.P. $=$ Rs. 80 and gain $=2.5 \%$
$ \text { S.P. }=\frac{\text { C.P. }(100+\text { gain \%) }}{100} $
$ =\frac{80(100+2.5)}{100} $
$ =\frac{80 \times 102.5}{100} $
$ =\frac{\text { Rs. } 80 \times 1025}{100 \times 10} $
$ =\text { Rs. } 82 $
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Question 203 Marks
Find the selling price, if: C.P. = Rs. 150 and loss = 20%
Answer
C.P. $=$ Rs. 150 and loss $=20 \%$
S.P. $=\frac{\text { C.P. }(100-\text { loss } \%)}{100}$
$=\frac{150(100-20)}{100}$
$=\frac{150 \times 80}{100}$
$=$ Rs. 120
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Question 213 Marks
Find the selling price, if: C.P. = Rs. 60 and loss = 12 1/2%
Answer
C.P. $=$ Rs. 60 and
$ \text { loss }=12 \frac{1}{2} \%=\frac{25}{2} \% $
$ \text { S.P. }=\frac{\text { C.P. }(100-\operatorname{loss} \%)}{100} $
$ =\frac{60\left(100-\frac{25}{2}\right)}{100} $
$ =\frac{60\left(\frac{200-25}{2}\right)}{100} $
$ =\frac{60 \times 175}{2 \times 100} $
$ =\text { Rs. } \frac{105}{2}=\text { Rs. } 52.50 $
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Question 223 Marks
Find the selling price, if: C.P. = Rs. 500 and gain = 25%
Answer

$\begin{aligned} & \text { C.P. }=\text { Rs. } 500 \text { and gain }=25 \% \\ & \text { S.P. }=\frac{\text { C.P. }(100+\text { gain } \%)}{100} \\ & =\frac{500(100+25)}{100} \\ & =\text { Rs. } \frac{500 \times 125}{100} \\ & =\text { Rs. } 625\end{aligned}$
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