# RD Sharma Solutions Class 7 Chapter 12 Profit and Loss

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Exercise 12.1

Question 1: Given the following values, find the unknown values:
(i) C.P. = Rs 1200, S.P. = Rs 1350 Profit/Loss?
(ii) C.P. = Rs 980, S.P. = Rs 940 Profit/Loss =?
(iii) C.P. = Rs 720, S.P. =? Profit = Rs 55.50
(iv) C.P. =? S.P. = Rs 1254, Loss = Rs 32
Solution 1:
(i) CP = Rs. 1200, SP = Rs. 1350
Clearly, we can find CP < SP.
So, there is condition of profit.
Profit = SP – CP
= Rs. (1350 – 1200)
= Rs. 150

(ii) CP = Rs. 980, SP = Rs. 940
Clearly, we can find CP > SP.
So, there is condition of loss.
Loss = CP – SP
= Rs. (980 – 940)
= Rs. 40

(iii) CP = Rs. 720, SP =? profit = Rs. 55.50
To find SP
Profit = SP – CP
55.50 = SP – 720
SP = (55.50 + 720)
= Rs. 775.50

(iv) CP =? SP = Rs. 1254, loss = Rs. 32
To find CP
Loss = CP – SP
32 = CP – 1254
CP = (1254 + 32)
= Rs. 1286

Question 2. Fill in the blanks in each of the following:
(i) C.P. = Rs 1265, S.P. = Rs 1253, Loss = Rs …….
(ii) C.P. = Rs……., S.P. = Rs 450, Profit = Rs 150
(iii) C.P. = Rs 3355, S.P. = Rs 7355……. = Rs……
(iv) C.P. = Rs……., S.P. = Rs 2390, Loss = Rs 5.50
Solution 2:
(i) Loss = Rs 12
Description:
CP = Rs. 1265, SP = Rs. 1253
Loss = CP – SP
= Rs. (1265 – 1253)
= Rs. 12
So, C.P. = Rs 1265, S.P. = Rs 1253, Loss = Rs 12

(ii) C.P. = Rs 300
Description:
CP =? SP = Rs. 450, profit = Rs. 150
Profit = SP – CP
150 = 450 – CP
CP = Rs. (450 – 150)
= Rs. 300
So, C.P. = Rs 300, S.P. = Rs 450, Profit = Rs 150

(iii) Profit = Rs 4000
Description:
CP = Rs. 3355, SP = Rs. 7355,
Here SP > CP, so profit.
Profit = SP – CP
Profit = Rs. (7355 – 3355)
= Rs. 4000
So, C.P. = Rs 3355, S.P. = Rs 7355, Profit = Rs. 4000

(iv) C. P. = Rs 2395.50
Description:
CP =?, SP = Rs. 2390, loss = Rs. 5.50
Loss = CP – SP
5.50 = CP – 2390
= Rs. (5.50 + 2390)
= Rs. 2395.50
So, C.P. = Rs, 2395.50, S.P. = Rs 2390, Loss = Rs 5.50

Question 3. Calculate the profit or loss and profit or loss percent in each of the following cases:
(i) C.P. = Rs 4560, S.P. = Rs 5000
(ii) C.P. = Rs 2600, S.P. = Rs 2470
(iii) C.P. = Rs 332, S.P. = Rs 350
(iv) C.P. = Rs 1500, S.P. = Rs 1500
Solution 3:
(i) CP = Rs. 4560, SP = Rs. 5000
Clearly, we can find SP > CP.
So, this is a condition of profit.
Profit = SP – CP
= Rs. (5000 – 4560)
Profit = Rs. 440
Profit percentage = {(Profit/CP) x 100} %
= {(440/4560) x 100} % = {0.0965 x 100} %
Profit in % = 9.65%

(ii)  CP = Rs. 2600, SP = Rs. 2470.
Clearly, we can find CP > SP.
So, this is a condition of loss.
Loss = CP – SP
= Rs. (2600 – 2470)
Loss = Rs. 130
Loss percentage = {(Loss/CP) x 100} %
= {(130/2600) x 100} % = {0.05 x 100} %
Loss in % = 5%

(iii) CP = Rs. 332, SP= Rs. 350.
Clearly, we cand find, SP > CP.
So, this is a condition of profit.
Profit = SP – CP
= Rs. (350 – 332)
Profit = Rs. 18
Profit percentage = {(Profit/CP) x 100} %
= {(18/332) x 100} % = {0.054 x 100} %
Profit in % = 5.4%

(iv) CP = Rs. 1500, SP = Rs. 1500
Clearly, we can find SP = CP.
So, neither profit nor loss.

Question 4. Find the gain or loss percent, when:
(i) C.P. = Rs 4000 and gain = Rs 40.
(ii) S.P. = Rs 1272 and loss = Rs 328
(iii) S.P. = Rs 1820 and gain = Rs 420.
Solution 4:
(i) CP = Rs. 4000, gain = Rs. 40
Gain in percent = {(Gain/CP) x 100) %
= {((40/4000) x 100} % = (0.01 x 100) %
Gain in percent  = 1%

(ii) SP = Rs. 1272, loss = Rs. 328
Loss = CP – SP
CP = Loss+ SP
= Rs. 328 + Rs. 1272
CP = Rs. 1600
Loss in percent = {(Loss/CP) x 100} %
= {(328/1600) x 100%
Loss in percent = 20.5%

(iii) SP = Rs. 1820, gain = Rs. 420
Gain = SP – CP
CP = 1820 – 420
CP= Rs. 1400
Gain in percent = {(Gain/CP) x 100} %
= {(420/1400) x 100 %
Gain  in percent = 30%

Question 5. Find the gain or loss percent, when:
(i) C.P. = Rs 2300, Overhead expenses = Rs 300 and gain = Rs 260.
(ii) C.P. = Rs 3500, Overhead expenses = Rs 150 and loss = Rs 146
Solution 5:
(i) CP = Rs. 2300, overhead expenses = Rs. 300 and gain = Rs. 260
As we know, Gain percentage = {Gain/((CP +Overhead expenses))} x 100
= {260/((2300+300 ) )} x 100 = {260/2600} x 100
Gain = 10%

(ii) CP = Rs. 3500, overhead expenses = Rs. 150 and loss = Rs. 146
As we know, Loss percentage = {Loss/((CP+Overhead expenses))} x 100
= {146/((3500+150))} x 100 = {146/3650} x 100
= 14600/3650
Loss = 4%

Question 6. A grain merchant sold 600 quintals of rice at a profit of 7%. If a quintal of rice cost him Rs 250 and his total overhead charges for transportation, etc. were Rs 1000 find his total profit and the selling price of 600 quintals of rice.
Solution 6:
1 quintal rice’s cost = Rs. 250
600 quintals of rice’s cost = 600 x 250 = Rs. 150000
CP = Rs. (150000 + 1000) = Rs. 151000
Profit percentage = (Profit/CP) x 100
7 = (Profit/151000) x 100
= 1510 x 7
Profit = Rs. 10570
SP = CP + profit
= Rs. (151000 + 10570)
SP = Rs. 161570

Question 7. Naresh bought 4 dozen pencils at Rs 10.80 a dozen and sold them for 80 paise each. Find his gain or loss percent.
Solution 7:
1 dozen pencils’ cost = Rs. 10.80
Thus, 4 dozen pencils’ cost  = 4 x 10.80
= Rs. 43.2
Also given that selling price of each pencil = 80 paise
Total number of pencils = 12 x 4 = 48
SP of 48 pencils = 48 x 80 paise
= 3840 paise
= Rs. 38.40
Clearly, we find that SP < CP.
So, the condition of loss.
Loss = CP – SP
= Rs. (43.2 – 38.4)
= Rs. 4.8
Loss % = (Loss/CP) x 100
= (4.8/43.2) x 100 = (480/43.2)
Loss = 11.11%

Question 8. A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain percent.
Solution 8:
CP of 1 dozen oranges is = Rs. 26
CP of 1 orange = (26/12) = Rs. 2.16
CP of 5 oranges = 2.16 x 5
= Rs. 10.8
Now, Given SP of 5 oranges = Rs. 13
So, Gain = SP – CP
= Rs. (13- 10.8)
= Rs. 2.2
Gain in percent = (Gain/CP) x 100
= (2.2/10.8) x 100
Gain = 20.3%

Question 9. Mr Virmani purchased a house for Rs 365000 and spent Rs 135000 on its repairs. If he sold it for Rs 550000, find his gain percent.
Solution 9:
Amount Mr. Virmani purchase the house = Rs. 365000
Amount he spent on repair = Rs. 135000
Total amount he spent on the house (CP) = Rs. (365000 + 135000)
= Rs. 500000
Given in the question SP of the house = Rs. 550000
Gain = SP – CP
= Rs. (550000 – 500000)
= Rs. 50000
Gain in percent = (Gain/CP)x 100
= (50000/500000) x 100 = 5000000/500000
Gain = 10%

Question 10. Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for Rs 910. Find her gain percent.
Solution 10:
CP of the Shikha’s wristwatch which she purchased , CP = Rs. 840
The price at which she sold it, SP = Rs. 910
Gain = SP – CP
= (910 – 840)
= Rs. 70
Now Gain in percent = (Gain/CP) x 100
=  (70/840) x 100 = 7000/840
Gain = 8.3%

Question 11. A business man makes a 10% profit by selling a toy costing him Rs 120. What is the selling price?
Solution 11:
Given in the question CP = Rs. 120
Profit in percent = 10

SP = {((100 +profit %))/100}x CP
={((100 +10))/100} x 120 = {((110))/100} x 120
= 1.1 x 120 = Rs. 132

Question 12. Harish purchased 50 dozen bananas for Rs 135. Five dozen bananas could not be sold because they were rotten. At what price per dozen should Harish sell the remaining bananas so that he makes a profit of 20%?
Solution 12:
Cost price of 50 dozens bananas which purchased by Harish , CP = Rs. 135
Bananas left after removing 5 dozen rotten bananas = 45 dozens
Effective CP of one dozen bananas = Rs. 135/45 = Rs. 3
Calculating the profit that Harish can make on each dozen bananas he sells 20% ( or 1/5),
Profit in percent = (Gain/CP) x100
To get a gain of 20% we give profit percent = 20
And substitute 20 = (Gain/135) x100
Gain = 270/10 = 27
SP = CP + Gain
SP = 27 + 135
SP = 162
Now, SP for 45 Dozen of bananas is Rs. 162.
Calculating for one dozen
= 162/45 = Rs. 3.6
Harish could sell the bananas for Rs. 3.60 a dozen to make a 20 percent profit.

Question 13. A woman bought 50 dozen eggs at Rs 6.40 a dozen. Out of these 20 eggs were found to be broken. She sold the remaining eggs at 55 paise per egg. Find her gain or loss percent.
Solution 13:
Cost of one dozen eggs = Rs. 6.40
Cost of 50 dozen eggs = 50 x 6.40 = Rs. 320
Total number of eggs = 50 x 12 = 600
Number of eggs left after removing the broken ones = 600 – 20 = 580
SP of 1 egg = 55 paise
So, SP of 580 eggs = 580 x 55 = 31900 paise
= Rs. 31900/100 = Rs. 319
Loss = CP – SP
= Rs. (320 – 319) = Rs. 1
Loss in percent = (Loss/CP) x 100 = (1/320) x 100
Loss = 0.31%

Question 14. Jyotsna bought 400 eggs at Rs 8.40 a dozen. At what price per hundred must she sell them so as to earn a profit of 15%?
Solution 14:
Cost of eggs per dozen = Rs. 8.40
Cost of 1 egg = (8.40/12) = Rs. 0.7
Cost of 400 eggs = 400 x 0.7 = Rs. 280
determining the price at which Jyotsna could sell the eggs in order to make a 15 percent profit,
15% of 280 + 280
= {(15/100) x 280} + 280 = {4200/100}+ 280
= 42 + 280 = Rs. 322
As a result, Jyotsna must sell the 400 eggs for Rs. 322 in order to make a 15% profit. As a result, the SP per hundred eggs is = Rs. 322/4 = Rs. 80.50.

Question 15. A shopkeeper makes a profit of 15% by selling a book for Rs 230. What is the C.P. and the actual profit?
Solution 15:
The SP of a book = Rs. 230
Profit percent = 15
CP = ((SP x 100))/((100 + profit %))
CP = ((230 x 100))/((100 + 15))
CP = 23000/115 = Rs. 200
Also, Profit = SP – CP
= Rs. (230 – 200) = Rs. 30
Actual profit = Rs. 30

Question 16. A bookseller sells all his books at a profit of 10%. If he buys a book from the distributor at Rs 200, how much does he sell it for?
Solution 16:
Profit percent = 10%
CP = Rs. 200
SP = {((100+profit %))/100} x CP
= {((100+10))/100} x 200
= {110/100} x 200 = Rs. 220
The book is sold for by the bookseller. Rs. 220.

Question 17. A floweriest buys 100 dozen roses at Rs 2 a dozen. By the time the flowers are delivered, 20 dozen roses are mutilated and are thrown away. At what price should he sell the rest if he needs to make a 20% profit on his purchase?
Solution 17:
Cost of 1 dozen roses = Rs. 2
Number of roses bought by the floweriest = 100 dozens
Thus, 100 dozen roses’ cost = 2 x 100 = Rs. 200
Roses remained after the mutilated ones were discarded = 80 dozens
Calculating the price at which the floweriest can sell the 80 dozen roses for a 20% profit
={((SP-CP))/CP} x100 = {((SP-200))/200} x 100
40 = SP – 200
SP = Rs. 240
Therefore, the SP of the roses should be Rs. 240/80 = Rs. 3 per dozen.

Question 18. By selling an article for Rs 240, a man makes a profit of 20%.What is his C.P.? What would his profit percent be if he sold the article for Rs 275?
Solution 18:
CP = Rs. x SP = Rs. 240
profit be Rs. P.
profit percent = 20%
Since Profit percent = (Profit/CP) x 100
20 = P/x x 100
P = 20x/100 = x/5
Profit = SP – CP = 240 – x
P = 240 – x
x/5 = 240 – x
240 = x + x/5
240 = 6x/5
x = 1200/6  = 200
So, CP = Rs. 200
New SP = Rs. 275 and CP = Rs. 200
Profit percent = {((SP-CP))/CP} x 100
{((275-200))/200} x 100 = 75/200 x 100
= 7500/200 = 37.5%