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Profit, Loss and Discount · ICSE STD 7 (ICSE - English Medium). 20 questions.

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20 questions · timed · auto-graded

Question 14 Marks
A dealer buys a T.V. set for Rs. 2500. He marks it at Rs. 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.
Answer
C.P. of a T.V. set $=$ Rs. 2500, M.P. $=$ Rs. 3200
Rate of discount $=10 \%$
$\therefore$ Total discount $=$ Rs. $3200 \times \frac{10}{100}=$ Rs. 320
(i) Sellin price $=$ Rs. 3200 - Rs. $320=$ Rs. 2880
(ii) Gain $=$ S.P. - C.P.
= Rs. 2880 - Rs. 2500 = Rs. 380
$\therefore$ Gain $\%=\frac{\text { gain } \times 100}{\text { C.P. }}$
$=\frac{380 \times 100}{2500}$
$=\frac{76}{5}=15 \frac{1}{5} \%=15.2$
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Question 24 Marks
An article is marked 60% above the cost price and sold at 20% discount. Find the profit percent made.
Answer
Let cost price of an article $=$ Rs. 100
$\therefore$ Marked price $=$ Rs. $100+60=$ Rs. 160
Rate of discount $=20 \%$
$ \begin{aligned} & \therefore \text { S.P. }=\frac{\text { M.P. } \times(100-\text { Discount % })}{100} \\ & =\frac{160 \times(100-20)}{100} \\ & =\frac{160 \times 80}{100}=\text { Rs. } 128 \end{aligned} $
Profit = S.P. - C.P.
$ =\text { Rs. } 128-100=\text { Rs. } 28 $
$\therefore$ Profit $\%=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$ =\frac{28 \times 100}{100}=28 \% $
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Question 34 Marks
The C.P. of 8 pens is same as S.P. of 10 pens. Calculate the profit or loss percent made, if all the pens bought are considered to be sold
Answer

$\begin{aligned} & \text { C.P. of } 8 \text { pens }=\text { S.P. of } 10 \text { pens }=\text { Rs. } 100 \text { (suppose) } \\ & \therefore \text { C.P. of } 1 \text { pen }=\frac{100}{8}=\text { Rs. } 12.50 \\ & \text { and S.P. of } 1 \text { pen }=\frac{100}{10}=\text { Rs. } 10 \\ & \therefore \text { Loss }=\text { C.P. }- \text { S.P. } \\ & =\text { Rs. } 12.50-\text { Rs. } 10=\text { Rs. } 2.50 \\ & \text { Loss } \%=\frac{\text { Loss } \times 100}{\text { C.P. }}=\frac{2.50 \times 100}{12.50} \\ & =\frac{250 \times 100 \times 100}{1250 \times 100}=20 \%\end{aligned}$
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Question 44 Marks
An article is bought for Rs. 1,200 and Rs. 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.
Answer
C.P. of an article $=$ Rs. 1200
Amount spent on transportation $=$ Rs. 100
(i) Total C.P. of that article $=$ Rs. $1200+100$
$ =\text { Rs. } 1300 $
(ii) Gain $=20 \%$, S.P. $=\frac{\text { C.P. } \times(100+\text { gain } \%)}{100}$
$ \begin{aligned} & =\frac{1300 \times(100+20)}{100} \\ & =\frac{1300 \times 120}{100}=\text { Rs. } 1560 \end{aligned} $
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Question 54 Marks
Find the cost price of an article, which is sold for Rs. 4050 at a loss of 10%. Also, find the new selling price of the article which must give a profit of 8%.
Answer
S.P. of an article $=$ Rs. 4050
Loss $=10 \%$
(i) $\therefore$ C.P. of the article $=\frac{\text { S.P } \times 100}{100-\operatorname{loss} \%}$
$=\frac{4050 \times 100}{100-10}$
$=\frac{4050 \times 100}{90}$
$=$ Rs. 4500
(ii) When gain $=8 \%$
$\therefore$ New S.P. of the article
$ =\frac{\text { C.P. }(100+\text { gain } \%)}{100} $
$ =\frac{4500(100+8)}{100} $
$ =\frac{4500 \times 108}{100}=\text { Rs. } 4860 $
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Question 64 Marks
A T.V. set is sold for Rs. 6800 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%.
Answer
S.P. of the T.V. set $=$ Rs. 6800
$ \text { Loss }=15 \% $
$ \begin{aligned} & \text { (i) } \therefore \text { C.P. }=\frac{\text { S.P } \times 100}{100-\operatorname{loss} \%} \\ & =\text { Rs. } \frac{6800 \times 100}{100-15} \\ & =\text { Rs. } \frac{6800 \times 100}{85}=\text { Rs. } 8000 \end{aligned} $
(ii) In second case, gain $=12 \%$
$ \begin{aligned} & \therefore \text { S.P. }=\frac{\text { C.P. }(100+12)}{100} \\ & =\text { Rs. } \frac{8000(100+12)}{100} \\ & =\text { Rs. } \frac{8000 \times 112}{100} \\ & =\text { Rs. } 8960 \end{aligned} $
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Question 74 Marks
On selling an article for Rs. 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%
Answer
S.P. of an article $=$ Rs. 2640
Gain $=10 \%$
(i) $\therefore$ C.P. $=\frac{\text { S.P. } \times 100}{100+\text { gain } \%}$
$=$ Rs. $\frac{2640 \times 100}{100+10}$
$=$ Rs. $\frac{2640 \times 100}{110}$
Rs. 2400
(ii) In second case, Gain $=15 \%$
$\therefore$ S.P. $=\frac{\text { C.P. }(100+\text { gain \%) }}{100}$
$=$ Rs. $\frac{2400(100+15)}{100}$
$=$ Rs. $\frac{2400 \times 115}{100}$
Rs. 2760 
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Question 84 Marks
An article is bought for ₹5,700 and ₹1,300 is spent on its repairing, transportion, etc. For how much should this article be sold in order to gain 20% on the whole.
Answer
C.P. of an article ₹ 5700
Amount spent on repair ₹ 1300
Total cost price (C.P.) ₹ 5700+ ₹ 1300= ₹ 7000
Gain $=20 \%$
$\therefore$ S.P. of an article $=\frac{\text { C.P. } \times(100+\text { Gain } \%)}{100}$
= ₹ $\frac{7000 \times(100+20)}{100}$
= ₹ $\frac{7000 \times 120}{100}$
= ₹ $\frac{840000}{100}$
= ₹ $8400$
$\therefore$ Selling price of an article (S.P.) = ₹ 8400
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Question 94 Marks
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.
Answer
$\because$ C.P. of one orange ₹ $\frac{80}{100}$= ₹ 0.8
and S.P. of one orange ₹  $\frac{100}{80}$= ₹ 1.25
Clearly, profit =₹ 1.25 - ₹ $0.8=$₹ 0.45
and profit 5 = ₹ $\frac{0.45}{0.8} \times 100$
$ \begin{aligned} & =\frac{45}{8} \times \frac{100 \times 10}{100} \\ & =\frac{450}{8}=56.25 \% \end{aligned} $
$\therefore$ Profit $\%=56.25 \%$
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Question 104 Marks
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.
Answer
$\because$ C.P. of one orange $=$ ₹ $\frac{350}{100}$ = 3.50
and S.P. of one orange = ₹ $\frac{48}{12}$ = 4
Clearly, Gain = ₹ 4 - ₹ 3.50 = ₹ 0.50
and gain percent $=\frac{\text { Gain } \times 100}{\text { C.P. }}$
= ₹ $\frac{0.50}{3.50} \times 100 \%=14 \frac{2}{7} \%$
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Question 114 Marks
The selling price of an article is 96% of its cost price. Find the loss or the gain as percent on the whole.
Answer
Let C.P. ₹ 100
S.P. $=96 \%$ of C.P.
= ₹ $\frac{96}{100} \times 100=$₹ 96
$\therefore$ Loss ₹ 100 - ₹ 96 = ₹ 4
and loss percent $=\frac{\operatorname{Loss} \times 100}{\text { C.P. }}$
$=\frac{4}{100} \times 100 \%$
$ =4 \% $
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Question 124 Marks
By selling an article for ₹825, a man loses equal to j 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 ₹ 1265.
Answer
S.P. of an article ₹ 825
Loss $=\frac{1}{3}$ of S.P. $=\frac{1}{3} \times 825$= ₹ 275
(i) $\therefore$ C.P. $=$ S.P. + Los
₹ 825+ ₹ 275= ₹ 1100
(ii) In second case,
S.P. ₹ 1265
$\therefore$ Gain $=$ S.P. - C.P.
₹ 1265 - ₹ 1100= ₹ 165
Gain $\%=\frac{\text { gain } \times 100}{\text { C.P. }}$
$=\frac{165 \times 100}{1100}=15 \%$
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Question 134 Marks
The cost price of an article is Rs. 1,200 and selling price is times of its cost price. Find:
(i) selling price of the article
(ii) profit or loss as a percent.
Answer

$\begin{aligned} & \text { Cost price (C.P. })=\text { Rs. } 1200 \\ & \therefore \text { S.P. }=\frac{5}{4} \text { of C.P. } \\ & =\frac{5}{4} \times 1200=\text { Rs. } 1500 \\ & \therefore \text { Gain }=\text { S.P. }- \text { C.P. } \\ & =\text { Rs. } 1500-\text { Rs. } 1200=\text { Rs. } 300 \\ & \therefore \text { Gain } \%=\frac{\text { gain } \times 100}{\text { C.P. }} \\ & =\frac{300 \times 100}{1200}=25 \%\end{aligned}$
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Question 144 Marks
A certain number of articles are bought at 3 for Rs. 150 and all of them are sold at 4 for Rs. 180. Find the loss or gain as percent.
Answer
L.C.M. of 3 and $4=12$
Let 12 articles are brought
$ \begin{aligned} & \therefore \text { C.P. of } 12 \text { articles }=\text { Rs. } \frac{150 \times 12}{3}=\text { Rs. } 600 \\ & \text { and S,P, of } 12 \text { articles = Rs. } \frac{180 \times 12}{4}=\text { Rs. } 540 \end{aligned} $
Loss $=$ C.P. - S.P.
$ =\text { Rs. } 600 \text { - Rs. } 540=\text { Rs. } 60 $
$ \text { Loss } \%=\frac{\text { Loss } \times 100}{\text { C.P. }}=\frac{60 \times 100}{600}=10 \% $
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Question 154 Marks
Oranges are bought at 5 for Rs. 10 and sold at 6 for Rs. 15. Find profit or loss as per cent.
Answer
L.C.M. of 5 and $6=30$
Let 30 oranges be brought.
$\therefore$ C.P. of 30 oranges $=\frac{30 \times 10}{5}=$ Rs. 60
and S.P. of 30 oranges $=\frac{30 \times 15}{6}=$ Rs. 75
Gain = S.P. - C.P.
$=$ Rs. $75-$ Rs. $60=$ Rs. 15
$\therefore$ Gain $\%=\frac{\text { gain } \times 100}{\text { C.P }}$
$=\frac{15 \times 100}{60}=25 \%$
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Question 164 Marks
The selling price of an article is Rs. 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.
Answer
(i) S.P. of an article $=$ Rs. 1200
$ \begin{aligned} & \therefore \text { C.P. }=\frac{5}{4} \text { of C.P. } \\ & =\frac{5}{4} \times 1200=\text { Rs. } 1500 \end{aligned} $
$ \begin{aligned} & \text { (ii) Loss = C.P. - S.P } \\ & =\text { Rs. } 1500-\text { Rs. } 1200=\text { Rs. } 300 \end{aligned} $
$ \text { Loss } \%=\frac{\text { Loss } \times 100}{\text { C.P. }} $
$ \begin{aligned} & =\frac{300 \times 100}{1500} \\ & =\frac{100}{5}=20 \% \end{aligned} $
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Question 174 Marks
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 is given by the shopkeeper.
(iii) the selling price.
(iv) profit percent made by the shopkeeper.
Answer

C.P. of an article = ₹ 300
Increase in price = 20%
(i)Marked price (M.P.)
$=\frac{\text { C.P. } \times(100+\text { increase } \%)}{100}$
= ₹ $\frac{300(100+20)}{100}$
= ₹ $\frac{300 \times 120}{100}$ = ₹ 360
(ii) Rate of discount = 10%
Amount of discounts
₹ $\frac{360 \times 10}{100}=$ ₹ 36
(iii) Selling price = M.P. discount
= ₹ 360 - ₹ 36 = ₹ 324
(iv) Net profit to the shopkeeper
= S.P. - C.P. = Rs. 324 - 300 = Rs. 24
Gain % = $\frac{\text { gain } \times 100}{\text { C.P. }}=\frac{24 \times 100}{300}=8 \%$

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Question 184 Marks
40 pens are bought at 4 for Rs. 50 and all of them are sold at 5 for Rs. 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?
Answer
(1) C.P. of 4 pens $=$ RS. 50
$\therefore$ C.P. of 40 pens $=\frac{50 \times 40}{4}=$ Rs. 500
and C.P. of 1 pen $=\frac{500}{40}=$ Rs. $\frac{25}{2}=$ Rs. 12.50
(ii) S.P. of pens $=$ Rs. 80
$\therefore$ S.P. of 1 pen $=$ Rs. $\frac{80}{5}=$ Rs. 16
(iii) Profit on one pen $=$ S.P. - C.P.
= Rs. $16.00-12.50$
$=$ Rs. 3.50
(iv) Profit percent $=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$=\frac{3.50 \times 100}{12.50}=\frac{350 \times 100}{1250}=28 \%$
(v) C.P. of 40 pens $=40 \times 12.50=$ Rs. 500
(vi) S.P. of 40 pens $=40 \times 16=$ Rs. 640
(vii) Profit on 40 pens $=$ S.P. - C.P.
= Rs. $640-500$
$=$ Rs. 140
(viii) Profit on 40 pens $=\frac{\text { Profit } \times 100}{\text { C.P. }}$
$=\frac{140 \times 100}{500}=28 \%$
Yes, the results of (iv) and (viii) are same.
We see that profit of on equal number of articles remains the same.
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Question 194 Marks
By selling two transistors for Rs. 00 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.
Answer
S.P. of first transistor $=$ Rs. 600
$ \text { Gain }=20 \% $
$ \begin{aligned} & \text { (i) } \therefore \text { C.P. }=\frac{\text { S.P. } \times 100}{100+\text { gain } \%} \\ & =\frac{600 \times 100}{100+20} \\ & =\frac{600 \times 100}{120}=\text { Rs. } 500 \end{aligned} $
S.P. of the second transistor $=$ Rs. 600
Loss $=20 \%$
$\therefore$ C.P. of the second transistor
$ \begin{aligned} & =\frac{\text { S.P. } \times 100}{100-\text { loss } \%} \\ & =\frac{600 \times 100}{100-20} \\ & =\text { Rs. } \frac{600 \times 100}{80}=\text { Rs. } 750 \end{aligned} $
$\therefore$ C.P. of the two transistors are Rs. 500 and Rs. 750
(ii) Total C.P. of both the transistors
$ \text { = Rs. } 500+\text { Rs. } 750=\text { Rs. } 1250 $
and total S.P. of both the transistors
$ =\text { Rs. } 600+\text { Rs. } 600=\text { Rs. } 1200 $
(iii) Total loss $=$ C.P. - S.P.
$ =1250-1200=\text { Rs. } 50 $
$\therefore$ loss $\%=\frac{\operatorname{loss} \times 100}{\text { C.P. }}$
$ =\frac{50 \times 100}{1250}=4 \% $
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Question 204 Marks
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.
Answer
Quantity of sweets bought $=120$
$ \therefore \text { C.P. of } 120 \text { sweets }=\frac{120 \times 20}{100}=\text { Rs. } 24 $
No. of sweets consumed $=18$
Balance sweets $=120-18=102$
$\therefore$ S.P. of 102 sweets
$ =\frac{102 \times 30}{100}=\frac{3060}{100}=\text { Rs. } 30.60 $
Gain = S.P. - C.P.
$=$ Rs. $30.60-$ Rs. $24=$ Rs. 6.60
Gain $\%=\frac{\text { gain } \times 100}{\text { C.P }}$
$ =\frac{6.60 \times 100}{24} $
$ =\frac{660 \times 100}{100 \times 24}=\frac{55}{2}=27.5 \% $
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