## RD Sharma Solutions Class 7 Chapter 12 Exercise 12.1

#### Exercise 12.1

**Q1. Given the following values, find the unknown values: **

**(i) C.P. = Rs 1200, S.P. = Rs 1350, Profit/Loss = ?**

**Solution:** CP = 1200, SP = 1350

As, CP < SP. So, there will be profit.

Profit = SP – CP

Profit = 1350 – 1200 = Rs. 150

**(ii) C.P. = Rs 980, S.P. = Rs 940, Profit/Loss = ?**

**Solution:Â **CP = 980, SP = 940

CP > SP. So, there will be loss.

Loss = 980 – 940 = Rs. 40

**(iii) C.P. = Rs 720, S.P. = ?, Profit = Rs 55.50**

**Solution:Â **CP = 720, profit = 55.50

Profit = SP â€“ CP

55.50 = SP – 720

SP = 55.50 + 720 = Rs. 775.50

**(iv) C.P. = ?, S.P. = Rs 1254, Loss = Rs 32 **

**Solution:Â **SP = 1254, loss = 32

Loss = CP – SP

32 = CP – 1254

CP = 1254 + 32 = Rs. 1286

**Q2. Fill in the blanks in each of the following: **

**(i) C.P. = Rs 1265, S.P. = Rs 1253, Loss = Rs ______Â **

**Solution:Â **CP = 1265, SP = 1253

Loss = CP – SP

Loss = 1265 – 1253 = Rs. 12

**(ii) C.P. = Rs______ , S.P. = Rs 450, Profit = Rs 150**

**Solution:** SP = Rs. 450, profit = 150

Profit = SP – CP

150 = 450 – CP

CP = 450 – 150

CP = Rs. 300

**(iii) C.P. = Rs 3355, S.P. = Rs 7355, profit/loss = Rs______**

**Solution:Â **CP = Rs. 3355, SP = 7355,

As, SP > CP.Â So, there will be profit.

Profit = SP – CP

Profit = 7355 – 3355

Profit = Rs. 4000

**(iv) C.P. = Rs _______, S.P. = Rs 2390, Loss = Rs 5.50 **

**Solution:**Â SP = 2390, loss = 5.50

Loss = CP – SP

Rs. 5.50 = CP – Rs. 2390

CP = 5.50 + 2390

CP = Rs. 2395.50

**Q3. 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**

**Solution:**Â CP = 4560, SP = 5000

As, SP > CP. So, there will be profit.

Profit = SP – CP

Profit = 5000 – 4560

Profit = Rs. 440

Profit % = {(Profit/CP) x 100}

Profit % = {(440/4560) x 100}

Profit % = {0.0965 x 100}

Profit % = 9.65%

**(ii) C.P. = Rs 2600, S.P. = Rs 2470**

**Solution:**Â CP = 2600, SP = 2470

As, CP > SP. So, there will be loss.

Loss = CP – SP

Loss = 2600 – 2470

Loss = 130

Now, calculating the profit percentage;

Profit % = {(Profit/CP) x 100}

Profit % = {(130/2600) x 100}%

Profit % = {0.05 x 100}%

Profit % = 5%

**(iii) C.P. = Rs 332, S.P. = Rs 350**

**Solution:**Â CP = 332, SP = 350

As, SP > CP. So, there will be profit.

Profit = SP – CP

Profit = 350 – 332

Profit = Rs. 18

Profit % = {(Profit/CP) x 100}

Profit % = {(18/332) x 100}

Profit % = {0.054 x 100}

Profit % = 5.4%

**(iv) C.P. = Rs 1500, S.P. = Rs 1500 **

**Solution:Â **CP = 1500, SP = 1500

As, SP = CP

So, neither profit nor loss.

**Q4. Find the gain or loss per cent, when:**

**Â (i) C.P. = Rs 4000 and gain = Rs 40.**

**Solution:**Â CP = 4000, gain = 40

Gain % = {(Gain/CP) x 100)

Gain % = {(40/4000) x 100}

Gain % = (0.01 x 100)

Gain % = 1%

**(ii) S.P. = Rs 1272 and loss = Rs 328**

**Solution:Â **SP = Rs. 1272, loss = Rs. 328

Loss = CP – SP

CP = Loss + SP

CP = 328 + 1272

CP = Rs. 1600

Loss % = {(Loss/CP) x 100}

Loss % = {(328/1600) x 100}

Loss % = 20.5%

**(iii) S.P. = Rs 1820 and gain = Rs 420. **

**Solution:Â **SP = 1820, gain = 420

Gain = SP – CP

CP = SP – Gain

CP = 1820 – 420

CP = Rs. 1400

Gain % = {(Gain/CP) x 100}

Gain % = {(420/1400) x 100

Gain % = 30%

**Q5. Find the gain or loss per cent, when: **

**(i) C.P. = Rs 2300, Overhead expenses = Rs 300 and gain = Rs 260.**

**Solution:Â **CP = 2300, overhead expenses = 300, gain = 260

Effective CP = CP + Overhead expenses

Effective CP = 2300 + 300

Effective CP = Rs. 2600

Gain % = {(Gain/Effective CP)} x 100

Gain % = {260/(2300 + 300} x 100

Gain % = {260/2600} x 100

Gain % = 10%

**(ii) C.P. = Rs 3500, Overhead expenses = Rs 150 and loss = Rs 146 **

**Solution: **CP = Rs. 3500, overhead expenses = Rs. 150, loss = Rs. 146

Effective CP = CP + Overhead expenses

Effective CP = 3500 + 150

Effective CP = 3605

Loss % = {( Loss/Effective CP)} x 100

Loss % = {146/(3500+ 150)} x 100

Loss % = {146/3650} x 100

Loss % = 14600/3650

Loss % = 4%

**Q6. 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:** It is given that;

Cost of 1 quintal of rice = Rs. 250

So, Cost of 600 quintals of rice = 600 x 250 = Rs. 150000

Overhead expenses = Rs. 1000

Effective CP = 150000 + 1000 = Rs. 151000

Profit % = (Profit/Effective CP) x 100

7 = (Profit/151000) x 100

Profit = 1510 x 7 = Rs. 10570

Profit = Rs. 10570

SP = Effective CP + profit = 151000 + 10570 = Rs. 161570

**Q7. 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: **It is given that the cost of 1 dozen pencils = Rs. 10.80

So, Cost of 4 dozen pencils = 4 x 10.80 = Rs. 43.2

Selling price of each pencil = 80 paise

Total number of pencils = 12 x 4 = 48Â Â [Since, 1 dozen = 12 pencils]

SP of 48 pencils = 48 x 80

SP of 48 pencils = 3840 paise

SP of 48 pencils = Rs. 38.40Â Â [Since, 100 Paisa = 1 Rs]

Here, SP < CP. So, there will be loss.

Loss = CP – SP = 43.2 – 38.4 = Rs. 4.8

Loss % = (Loss/CP) x 100

Loss % = (4.8/43.2) x 100

Loss % = 480/43.2

Loss % = 11.11%

**Q8. A vendor buys oranges at Rs 26 per dozen and sells them at 5 for Rs 13. Find his gain percent. **

**Solution:Â **CP of 1 dozen oranges = Rs. 26

CP of 1 orange = 26/12 = Rs. 2.16Â Â Â Â [As, 1 dozen = 12 oranges]

CP of 5 oranges = 2.16 x 5 = Rs. 10.8

Vendor sells 5 oranges at Rs. 13.

So, SP of 5 oranges = Rs. 13

CP < SP. So, there will be gain.

Gain = SP – CP = 13- 10.8 = Rs. 2.2

Gain % = (Gain/CP) x 100

Gain % = (2.2/10.8) x 100

Gain % = 20.3%

**Q9. 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:Â **Amount paid by Mr. Virmani tp purchase the house = Rs. 365000

Amount spent on repair = Rs. 135000

Total amount spent on the house (CP) = 365000 + 135000 = Rs. 500000

The house is sold atÂ Rs 550000.

So, SP of the house = Rs. 550000

CPÂ < SP. So, there will be profit.

Gain = SP – CP = 550000 – 500000 = Rs. 50000

Gain % = (Gain/CP) x 100

Gain % = (50000/500000) x 100

Gain % = 5000000/500000

Gain % = 10%

**Q10. Shikha purchased a wrist watch for Rs 840 and sold it to her friend Vidhi for Rs 910. Find her gain percent**.

**Solution:Â **The cost price of the wristwatch, CP = Rs. 840

Selling price of the wristwatch, SP = Rs. 910

CPÂ < SP. So, there will be profit.

Gain = SP – CP = (910 – 840) = Rs. 70

Gain % = (Gain/CP) x 100

Gain % = (70/840) x 100

Gain % = 7000/840

Gain % = 8.3%

**Q11. A business man makes a 10% profit by selling a toy costing him Rs 120. What is the selling price? **

**Solution:** It is given that;

CP = Rs. 120

Profit % = 10%

Profit % = (Profit/CP) x 100

10 =Â (Profit/120) x 100

Profit = (10Â Ã— 120)/100

Profit = Rs. 12

Profit = SP – CP

12 = SP – 120

SP = Rs. 132

**Q12. 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:Â **Total number of bananas = 50 dozen

No. of Bananas which were rotten = 5 dozen

Bananas left after removing rotten bananas = 50 – 5 = 45 dozens

Cost price of 50 dozens bananas, CP = Rs. 135

Price at which Harish should sell 45 dozen bananas to make a profit of 20%;

Profit % = (Gain/CP) x 100

20 = (Gain/135) x 100

Gain = 270/10 = Rs. 27

We know that;

Gain = SP – CP

27 = SP – 135

SP = Â 27 + 135

SP = Rs. 162

SP of 45 dozens of bananas = Rs. 162

SP for 1 dozen of bananas = 162/45 = Rs. 3.6

Harish should sell the bananas at Rs. 3.60 a dozen in order to make a profit of 20%.

**Q13**. **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:Â **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

Broken eggs = 20

Number of eggs left after removing the broken eggs = 600 – 20 = 580

SP of 1 egg = 55 paise

So, SP of 580 eggs = 580 x 55

SP of 580 eggs = 31900 paise

SP of 580 eggs = Rs. 31900/100

SP of 580 eggs = Rs. 319Â Â Â [As, 100 Paisa = 1 Rs]

Loss = CP – SP = 320-319 = Rs. 1

Loss % = (Loss/CP) x 100

Loss % = (1/320) x 100

Loss % = 0.31%

**Q14. 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:Â **Cost of 1 dozen of eggs = Rs. 8.40

Cost of 1 egg = 8.40/12 = Rs. 0.7Â Â Â Â [Since, 1 dozen = 12 eggs]

Cost of 400 eggs = 400 x 0.7 = Rs. 280

Price at which Jyotsana should sell the 400 eggs to earn a profit of 15%,

Profit % = (Gain/CP) x 100

15 = (Gain/280) Ã— 100

Gain = (15Â Ã— 280)/100

Gain = Rs. 42

We know that,Â Gain = SP – CP

42 = SP – 280

SP = Rs. 322

The SP of 400 eggs = 322

SP for 100 eggs = (322Â Ã— 100)/400 = Rs. 80.50

Therefore, the SP per one hundred eggs is Rs. 80.50.

**Q15. A shopkeeper makes a profit of 15% by selling a book for Rs 230. What is the C.P. and the actual profit ? **

**Solution:** It is given that;

SP of a book = Rs. 230

Profit % = 15%

CP = ?, Profit = ?

Profit % = (Profit/CP) x 100

15 = {(SP – CP)/CP} Ã— 100Â Â Â Â Â Â Â Â Â [Since, Profit = SP – CP]

0.15 = (230 – CP)/CP

0.15 CP = 230 – CP

1.15 CP = 230

CP = 200

We know that Profit = SP – CP

Profit = 230 – 200

Profit = Rs. 30

**Q16. 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: **It is given that;

Profit % = 10%, CP = Rs. 200

SP = ?

Profit % = (Profit/CP) x 100

10 = (Profit/200)Â x 100

Profit = (10Â x 200)/100

Profit = Rs. 20

As we know that; Profit = SP – CP

20 = SP – 200

SP = Rs. 220

The bookseller sells the book for Rs. 220.

**Q17. A flowerist 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:** It is given that, cost of 1 dozen roses = Rs. 2

Florist bought 100 dozens of roses.

Thus, cost price of 100 dozen roses = 2 x 100 = Rs. 200

No. of roses thrown away = 20 dozen

Roses left after discarding the mutilated ones = 100 – 20 = 80 dozens

Price at which the florist should sell the 80 dozen roses in order to make a profit of 20%,

Profit % = (Profit/CP) x 100

20 = (Profit/200)Â x 100

Profit = (20Â x 200)/100

Profit = Rs. 40

As we know that; Profit = SP – CP

40 = SP – 200

SP = Rs. 240

Therefore, flowerist should sell the rest of the flowers at Rs. 240 to make 20% profit on his purchase.

**Q18. 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:** It is given that;

SP = 240, P% = 20%

CP = ?

Profit % = (Profit/CP) x 100

20 = {(SP – CP)/CP} x 100

0.2 = (240 – CP)/CP

0.2 CP = 240 – CP

1.2 CP = 240

CP = Rs. 200

New SP =Â Rs. 275

CPÂ < SP. So, there will be profit

Profit = SP – CP = 275 – 200 = Rs. 75

Profit % = (Profit/CP) x 100

Profit % = (75/200) x 100

Profit % = 37.5%