RD Sharma Solutions for Class 7 Maths Chapter 12 Profit And Loss Free Online
Exercise: 12.1 Page No.: 12.8
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:
(i) Given CP = Rs. 1200, SP = Rs. 1350
Clearly CP < SP. So, profit.
Profit = SP – CP
= Rs. (1350 – 1200)
= Rs. 150
(ii) Given CP = Rs. 980, SP = Rs. 940
Clearly CP > SP. So, loss.
Loss = CP – SP
= Rs. (980 – 940)
= Rs. 40
(iii) CP = Rs. 720, SP =?, profit = Rs. 55.50
Profit = SP – CP
55.50 = SP – 720
SP = (55.50 + 720)
= Rs. 775.50
(iv) CP =?, SP = Rs. 1254, loss = Rs. 32
Loss = CP – SP
32 = CP – 1254
CP = (1254 + 32)
= Rs. 1286
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:
(i) Loss = Rs 12
Explanation:
Given CP = Rs. 1265, SP = Rs. 1253
Loss = CP – SP
= Rs. (1265 – 1253)
= Rs. 12
(ii) C.P. = Rs 300
Explanation:
Given CP = 7, SP = Rs. 450, profit = Rs. 150
Profit = SP – CP
150 = 450 – CP
CP = Rs. (450 – 150)
= Rs. 300
(iii) Profit = Rs 4000
Explanation:
Given CP = Rs. 3355, SP = Rs. 7355,
Here SP > CP, so profit.
Profit = SP – CP
Profit = Rs. (7355 – 3355)
= Rs. 4000
(iv) C. P. = Rs 2395.50
Explanation:
Given CP = 7, SP = Rs. 2390, loss = Rs. 5.50
Loss = CP – SP
5.50 = CP – 2390 CP
= Rs. (5.50 + 2390)
= Rs. 2395.50
3. Calculate the profit or loss and profit or loss per cent 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:
(i) Given CP = Rs. 4560, SP = Rs. 5000
Here, clearly SP > CP. So, profit.
Profit = SP – CP
= Rs. (5000 – 4560)
= Rs. 440
Profit % = {(Profit/CP) x 100} %
= {(440/4560) x 100} %
= {0.0965 x 100} %
Profit % = 9.65%
(ii) Given CP = Rs. 2600, SP = Rs. 2470.
Here, clearly CP > SP. So, loss.
Loss = CP – SP
= Rs. (2600 – 2470)
= Rs. 130
Loss % = {(Loss/CP) x 100} %
= {(130/2600) x 100} %
= {0.05 x 100} %
Loss % = 5%
(iii) Given CP = Rs. 332, SP= Rs. 350.
Here, clearly SP > CP. So, profit.
Profit = SP – CP
= Rs. (350 – 332)
= Rs. 18
Profit% = {(Profit/CP) x 100} %
= {(18/332) x 100} %
= {0.054 x 100} %
Profit % = 5.4%
(iv) Given CP = Rs. 1500, SP = Rs. 1500
Here clearly SP = CP.
So, neither profit nor loss.
4. Find the gain or loss per cent, 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:
(i) Given CP = Rs. 4000, gain = Rs. 40
Gain % = {(Gain/CP) x 100) %
= {(40/4000) x 100} %
= (0.01 x 100) %
Gain % = 1%
(ii) Given SP = Rs. 1272, loss = Rs. 328
Loss = CP – SP
Hence, CP = Loss+ SP
= Rs. 328 + Rs. 1272
= Rs. 1600
Loss % = {(Loss/CP) x 100} %
= {(328/1600) x 100%
Loss % = 20.5%
(iii) Given SP = Rs. 1820, gain = Rs. 420
Gain = SP – CP
CP = 1820 – 420
= Rs. 1400
Gain % = {(Gain/CP) x 100} %
= {(420/1400) x 100 %
Gain % = 30%
5. Find the gain or loss per cent, 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:
(i) Given CP = Rs. 2300, overhead expenses = Rs. 300 and gain = Rs. 260
We know that Gain % = {(Gain/ (CP + overhead expenses)} x 100
= {260/ (2300 + 300} x 100
= {260/2600} x 100
Gain = 10%
(ii) Given CP = Rs. 3500, overhead expenses = Rs. 150 and loss = Rs. 146
We know that Loss % = {(Loss/ (CP + overhead expenses)} x 100
= {146/ (3500+ 150)} x 100
= {146/3650} x 100
= 14600/3650
Loss = 4%
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:
Given Cost of 1 quintal of rice = Rs. 250
Cost of 600 quintals of rice = 600 x 250 = Rs. 150000
Overhead expenses = Rs. 1000
CP = Rs. (150000 + 1000) = Rs. 151000
Profit % = (Profit/CP) x 100
7 = (Profit /151000) x 100
Profit = 1510 x 7
Profit = Rs. 10570
Now SP = CP + profit
= Rs. (151000 + 10570)
SP = Rs. 161570
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:
Given Cost of 1 dozen pencils = Rs. 10.80
Therefore cost of 4 dozen pencils = 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
Here, clearly SP < CP.
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%
8. A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain percent.
Solution:
Given CP of 1 dozen oranges = Rs. 26
CP of 1 orange = 26/12
= Rs. 2.16
CP of 5 oranges = 2.16 x 5
= Rs. 10.8
Now, SP of 5 oranges = Rs. 13
Gain = SP – CP
= Rs. (13- 10.8)
= Rs. 2.2
Gain %= (Gain/CP) x 100
= (2.2/10.8) x 100
Gain = 20.3%
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:
Given Mr. Virmani spent to 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 SP of the house = Rs. 550000
Gain = SP – CP
= Rs. (550000 – 500000)
= Rs. 50000
Gain % = (Gain/CP) x 100
= (50000/500000) x 100
= 5000000/500000
Gain = 10%
10. Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for Rs 910. Find her gain percent.
Solution:
Given CP of the wristwatch that Shikha purchased, CP = Rs. 840
The price at which she sold it, SP = Rs. 910
Gain = SP – CP
= (910 – 840)
= Rs. 70
Now Gain % = (Gain/CP) x 100
= (70/840) x 100
= 7000/840
Gain = 8.3%
11. A business man makes a 10% profit by selling a toy costing him Rs 120. What is the selling price?
Solution:
CP = Rs. 12
Profit % = 10
We now that
SP = {(100 + profit %) /100} x CP = {(100+ 10)/100} x 120
= {(110/100)} x 120 = 1.1 x 120
= Rs. 132
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:
Given cost price of 50 dozens bananas that Harish purchased, 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 price at which Harish should sell each dozen bananas to make a profit of 20% (or 1/5), we get
Profit % = (Gain/CP) x100
To get a gain of 20% we give profit % = 20
And substitute 20 = (gain/135) x100
Gain = 270/10 = 27
We know; SP = CP + Gain
SP = 27 + 135
SP = 162
Now that SP is for 45 Dozens of bananas
Calculating for one dozen
= 162/45
= Rs. 3.6
Harish should sell the bananas at Rs. 3.60 a dozen in order to make a profit of 20%.
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:
Given 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 % = (Loss/CP) x 100
= (1/320) x 100
Loss = 0.31%
14. Jyotsana 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:
Given 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
Calculating the price at which Jyotsana should sell the eggs to earn a profit of 15%,
We get 15% of 280 + 280
= {(15/100) x 280} + 280
= {4200/100} + 280
= 42 + 280
= Rs. 322
So, Jyotsana must sell the 400 eggs for Rs. 322 in order to earn a profit of 15%. Therefore, the SP per one hundred eggs = Rs. 322/4 = Rs. 80.50.
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:
Given that the SP of a book = Rs. 230
Profit % = 15
Since
CP = (SP x 100) + (100 + profit %)
CP = (230x 100) + (100 + 15)
CP = 23000 + 115 = Rs. 200
Also, Profit = SP – CP = Rs. (230 – 200) = Rs. 30
Actual profit = Rs. 30
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:
Given profit % = 10% CP = Rs. 200
Since SP = {(100 + profit %) /100} x CP
= {(100 + 10)/100} x 200
= {110/100} x 200 = Rs. 220
The bookseller sells the book for Rs. 220.
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:
Given cost of 1 dozen roses = Rs. 2
Number of roses bought by the florist = 100 dozens
Thus, cost price of 100 dozen roses = 2 x 100 = Rs. 200
Roses left after discarding the mutilated ones = 80 dozens
Calculating the price at which the florist should sell the 80 dozen roses in order to make a profit of 20%, we have
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.
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:
Let CP = Rs. x SP = Rs. 240
Let profit be Rs. P.
Now, profit % = 20%
Since Profit % = (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 = 6×15
x = 1200/6
x = 200
So, CP = Rs. 200
New SP = Rs. 275 and CP = Rs. 200
Profit % = {(SP – CP)/CP} x 100
{(275 – 200)1200} x 100 = (75/200) x 100
= 7500/200
= 37.5%
