The document RD Sharma Solutions - Chapter 13 - Proft, Loss, Discount and Value Added Tax (VAT) (Part -1), Class8 Class 8 Notes | EduRev is a part of the Class 8 Course RD Sharma Solutions for Class 8 Mathematics.

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**PAGE NO 13.11:**

**Question 1:**

**A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain percent.**

**ANSWER:**

C.P of pen = Rs. 90

S.P of pen = Rs. 100

Gain = SP âˆ’CP

Gain = 100âˆ’90 = Rs. 10

Gain% =

**PAGE NO 13.11:**

**Question 2:**

**Rekha bought a saree for Rs 1240 and sold it for Rs 1147. Find her loss and loss percent.**

**ANSWER:**

C.P of saree = Rs. 1240

S.P of saree = Rs. 1147

Loss = CPâˆ’SP

Loss = Rs.(1240âˆ’1147) = Rs. 93

loss% =

= 7.5%

**PAGE NO 13.11:**

**Question 3:**

**A boy buys 9 apples for Rs 9.60 and sells them at 11 for Rs 12. Find his gain or loss percent.**

**ANSWER:**

C.P of 9 apples = Rs 9.60

âˆ´ C.P of 1 apple = Rs 9.609 = Rs16/15

S.P of 11 apples = Rs 12

âˆ´ S.P of 1 apple = Rs 12/11

Clearly, S.P of 1 apple >C.P of 1 apple

So, we get profit on selling apples

**PAGE NO 13.11:**

**Question 4:**

**The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.**

**ANSWER:**

Let the cost price of one article be Rs. C and the selling price be Rs. S

Therefore, 10C = 9S

C = 9/10.S

So, the cost price is less than the selling price.

S.P. =

1000/9 = 100 + Profit

00/9âˆ’100 = Profit%

Profit% =

=

Therefore, the required profit percent is

**PAGE NO 13.11:**

**Question 5:**

**A retailer buys a radio for Rs 225. His overhead expenses are Rs 15. If he sells the radio for Rs 300, determine his profit percent.**

**ANSWER:**

Radio costs = Rs. 225

Overhead expenses = Rs. 15

C.P = Rs. (225 + 15) = Rs. 240

S.P = Rs. 300

Profit = SPâˆ’CP

= Rs. (300âˆ’240)

= Rs. 60

Profit% = Profit/C.P Ã— 100

= 60/240 Ã— 100 = 25%

**PAGE NO 13.11:**

**Question 6:**

**A retailer buys a cooler for Rs 1200 and overhead expenses on it are Rs 40. If he sells the cooler for Rs 1550, determine his profit percent.**

**ANSWER:**

Cooler costs = Rs.1200

Overhead expenses = Rs. 40

C.P = Rs. (1200 + 40) = Rs. 1240

S.P = Rs. 1550

Profit = SPâˆ’CP

= Rs. (1550âˆ’1240)

= Rs. 310

Profit% = Profit/C.P Ã— 100

= 310/1240 Ã— 100

= 25%

**PAGE NO 13.11:**

**Question 7:**

**A dealer buys a wristwatch for Rs 225 and spends Rs 15 on its repairs. If he sells the same for Rs 300, find his profit percent.**

**ANSWER:**

A dealer buys a wrist watch for Rs. 225

Money spent on repairing the watch = Rs. 15

Therefore,C.P = Rs. (225 + 15) = Rs. 240

S.P = Rs. 300

Profit = SPâˆ’CP

= Rs. (300âˆ’240)

= Rs. 60

Profit% = Profit/C.P Ã— 100

= 60/240 Ã— 100

= 25%

**PAGE NO 13.11:**

**Question 8:**

**Ramesh bought two box es for Rs 1300. He sold one box at a profit of 20% and the other box at a loss of 12%. If the selling price of both box es is the same, find the cost price of each box .**

**ANSWER:**

Let the cost price of the first box be Rs. x .

Therefore, the cost of the second box will be Rs. (1300âˆ’ x )

Profit on the first box = 20 %

Loss on the second box = 12%

SP of the first box = CP

SP = x (120/100)

SP of the first box = Rs.120 x 100 = Rs.6 x 5

SP of the second box = CP

S.P of the second box =

Since S.P of both the box are equal,

150 x = 143000âˆ’110 x

260 x = 143000

x = 143000/260

x = 550

Therefore, the cost price of the first box is Rs. 550.

The cost price of the second box will be Rs.(1300âˆ’550) = Rs. 750

**PAGE NO 13.11:**

**Question 9:**

**If the selling price of 10 pens is equal to cost price of 14 pens, find the gain percent.**

**ANSWER:**

Let the cost price of one pen be Rs. C, and the selling price be Rs. S

Therefore, 10S = 14C

C = 10/14.S

However, the cost price is less than the selling price.

S.P. =

1400/10 = 100 + profit%

140âˆ’100 = profit%

Profit% = 40 = 40%

Therefore, the required profit percent is 40%.

**PAGE NO 13.11:**

**Question 10:**

**If the cost price of 18 chairs be equal to selling price of 16 chairs, find the gain or loss percent.**

**ANSWER:**

Let the cost price of one chair be Rs. C, and selling price be Rs. S

Therefore, 18C = 16S

C = 16/18.S

As cost price is less than the selling price,

S.P. =

1800/16 = 100 + profit%

180016âˆ’100 = profit%

Profit% =

= 200/16 = 12.5

Therefore, the required profit percent is 12.5%.

**PAGE NO 13.11:**

**Question 11:**

**If the selling price of 18 oranges is equal to the cost price of 16 oranges, find the loss percent.**

**ANSWER:**

Let the cost price of one orange be Rs. C, and its selling price be Rs. S

Therefore, 16C = 18S

C = 18/16.S

As cost price is more than the selling price,

S.P. =

1600/18 = 100âˆ’loss%

Loss% = 100âˆ’1600/18

Loss% =

= 200/18 = 100/9

=

Therefore, the loss percent is %.

**PAGE NO 13.11:**

**Question 12:**

**Ravish sold his motorcycle to Vineet at a loss of 28%. Vineet spent Rs 1680 on its repairs and sold the motor cycle to Rahul for Rs 35910, thereby making a profit of 12.5%, find the cost price of the motor cycle for Ravish.**

**ANSWER:**

Let the cost price of the motorcycle for Ravish be Rs. x .

Loss% = 28%

Therefore, SP = CP

SP = Rs. x (72/100)

Selling price of the motorcycle for Ravish = Cost price of the motorcycle for Vineet

Money spent on repairs = Rs. 1680

Therefore, total cost price of the motorcycle for Vineet = Rs.( x (72/100) + 1680)

Selling price of the motorcycle for Vineet = Rs. 35910

Profit% = 12.5%

SP = CP

â‡’ 35910 Ã— 100 Ã— 100 = (72 x + 168000)(112.5)

â‡’ 359100000 = 8100 x + 18900000

â‡’ 340200000 = 8100 x

â‡’ x = Rs. 42000

Therefore, Ravish bought the motorcycle for Rs. 42000

**PAGE NO 13.12:**

**Question 13:**

**By selling a book for Rs 258, a bookseller gains 20%. For how much should he sell it to gain 30%?**

**ANSWER**:

Selling price of the book = Rs. 258

Gain% = 20%

Since, C.P =

= 25800/120

= Rs. 215

Let the bookseller sells it for Rs. x

So, S.P =

= Rs. 279.50

Therefore, the bookseller must sell the book at Rs 279.50 to make 30% profit.

**PAGE NO 13.12:**

**Question 14:**

**A defective briefcase costing Rs 800 is being sold at a loss of 8%. If the price is further reduced by 5%, find its selling price.**

**ANSWER:**

C.P of the briefcase = Rs. 800

Loss = 8%

S.P = CP

= 800 Ã— 0.92

= Rs. 736

If the price is further reduced by 5%, the selling price of the briefcase will be

= Rs.(736âˆ’736 Ã— 5/100)

= 736 Ã— 0.95

= Rs. 699.20

Thus, the selling price of the briefcase will be Rs 699.20.

**PAGE NO 13.12:**

**Question 15:**

**By selling 90 ball pens for Rs 160 a person loses 20%. How many ball pens should be sold for Rs 96 so as to have a profit of 20%?**

**ANSWER:**

S.P of 90 ball pens = Rs. 160

Loss = 20%

Therefore, C.P = SP

= Rs. 200

Now,S.P of 90 ball pens = Rs. 96

Profit = 20%

C.P = SP

CP =

= 9600/120

= Rs. 80

Rs. 200 is the C.P of 90 ball pens.

Therefore, Rs. 80 is the C.P of = = 36 ball pens

Thus, 36 ball pens should be sold at Rs. 96 to earn a profit of 20%.

**PAGE NO 13.12:**

**Question 16:**

**A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs 36.75 less, he would have gained 30%. Find the cost price of the article.**

**ANSWER:**

Let the C.P of the article be Rs. x .

Original S.P = x + 25/100.x

= Rs. 5x/4

If he purchased it at 20% less,C.P = x âˆ’20/100.x

= Rs. 4x/5

He sold the article at Rs 36.75 less.

So, the selling price = Rs. 5x/4âˆ’36.75

Given that he would have gained 30% selling at that price.

Therefore, gain% =

S.Pâˆ’C.P = 5x/4âˆ’36.75âˆ’4 x 5

= 5x/4âˆ’4x/5âˆ’36.75

âˆ’36.75

= 9x/20âˆ’36.75

So, gain% =

225 x âˆ’18375 = 120 x

105 x = 18375 x

= 18375/105

= 175

So, the cost price of the article is Rs. 175.

**PAGE NO 13.12:**

**Question 17:**

**A dishonest shopkeeper professes to sell pulses at his cost price but uses a false weight of 950 gm for each kilogram. Find his gain percent.**

**ANSWER:**

He sells 950gm pulses and gets a gain of 50gm.

If he sells 100gm of pulses, he will gain = 509/50 Ã— 100

= 5000/950

**PAGE NO 13.12:**

**Question 18:**

**A dealer bought two tables for Rs 3120. He sold one of them at a loss of 15% and other at a gain of 36%. Then, he found that each table was sold for the same price. Find the cost price of each table.**

**ANSWER:**

Given that the selling price is same for both the tables.

Let the C.P of 1 table be Rs. x , then the C.P of the other will be Rs.(3120âˆ’ x ).

Loss on the first table = 15%

Therefore, S.P = C.P

S.P = 85x/100 = Rs. 0.85 x

Gain on the second table = 36%

Therefore, S.P = C.P

S.P = Rs. 1.36(3120âˆ’ x )

Since both tables have the same S.P,

So, 0.85 x = 1.36(3120âˆ’ x )

0.85 x = 4243.20âˆ’1.36 x

2.21 x = 4243.20

x = 4243.20/2.21

x = Rs. 1920

So,the cost price of the first table is Rs. 1920.

Cost price of the second table = Rs. ( 3120âˆ’1920) = Rs. 1200

**PAGE NO 13.12:**

**Question 19:**

**Mariam bought two fans for Rs 3605. She sold one at a profit of 15% and the other at a loss of 9%. If Mariam obtained the same amount for each fan, find the cost price of each fan.**

**ANSWER:**

It is given that the S.P is same for both the fans.Let C.P of the first fan be Rs. x

Therefore, C.P of the second fan = Rs. (3605âˆ’ x )

Profit on the first fan = 15%

Loss on the second fan = 9%

For the first fan,S.P = C.P

For the second fan,S.P = C.P

= (3605âˆ’ x )(91/100)

Since S.P of both the fans is the same,23x/20 = (3605âˆ’ x )(91/100)

2300 x = 91(72/100âˆ’20 x )2300

x = 6561100âˆ’1820 x

4120 x = 6561100

x = Rs.1592.50

Thus, C.P of the first fan is Rs. 1592.50.C.P of the second fan = Rs. (3605âˆ’1592.50) = Rs. 2012.50

**PAGE NO 13.12:**

**Question 20:**

**Some toffees are bought at the rate of 11 for Rs 10 and the same number at the rate of 9 for Rs 10. If the whole lot is sold at one rupee per toffee, find the gain or loss percent on the whole transaction.**

**ANSWER:**

Let the total number of toffees bought be x.

Let x/2 toffees at the rate of 11 are bought for Rs.10, and x/2 toffees at the rate of 9 are bought for Rs.10

Total money spent on buying the toffees = (x/2)(10/11) + (x/2)(10/9)

= 200x/198

= 100/99 x

It is given that x toffees are sold at one rupee per toffee.

Therefore, the selling price of x toffees = Rs. x Ã— 1 = Rs. x

As C.P is more than S.P, it will be a loss.

Loss = C.Pâˆ’S.P

= x/99

Loss% = Loss/C.P Ã— 100

Total loss on the whole transaction would be 1%.

**PAGE NO 13.12:**

**Question 21:**

**A tricycle is sold at a gain of 16%. Had it been sold for Rs 100 more, the gain would have been 20%. Find the C.P. of the tricycle.**

**ANSWER:**

Let the S.P of the tricycle be Rs. x and C.P be Rs. y Gain% = 16%

S.P = C.P

Then we have, x = y +

x = y + 0.16y

x = 1.16y

When S.P increases by Rs. 100,

we get

â‡’ x + 100 = y +

Putting x = 1.6y, we get

â‡’ 1.16y + 100 = y + 0.2y

1.16y + 100 = 1.2y

0.04y = 100

y = 100/0.04

= 2500

Thus, C.P of the tricycle is Rs. 2500.

**PAGE NO 13.12:**

**Question 22:**

**Shabana bought 16 dozen ball bens and sold them at a loss equal to S.P. of 8 ball pens. Find (i) her loss percent (ii) S.P. of 1 dozen ball pens, if she purchased these 16 dozen ball pens for Rs 576.**

**ANSWER:**

(i) Number of pens bought = 16 Ã— 12 = 192

Let the S.P of one pen be Rs. x .

Therefore, S.P of 192 pens = Rs. 192 x S.P of 8 pens = Rs. 8 x

It is given that S.P of 8 pens is equal to the loss on selling 192 pens.

Therefore, loss = Rs. 8 x C.P of 192 pens = Rs. 576

So, loss = C.Pâˆ’S.P

8 x = 576âˆ’192 x

200 x = 576

x = 576/200 = 2.88

Therefore, loss = 8(2.88) = Rs. 23.04

= 4%

(ii) S.P of 1 pen = Rs. 2.88

Therefore, S.P of 1 dozen pens = 12x

= 12 Ã— 2.88

= Rs. 34.56

**PAGE NO 13.12:**

**Question 23:**

**The difference between two selling prices of a shirt at profits of 4% and 5% is Rs 6. Find (i) C.P. of the shirt (ii) the two selling prices of the shirt**

**ANSWER:**

Let the C.P of both the shirts be Rs. x .C.P = Rs. x

For shirt 1:

Profit is 4%:

Profit% = Profit/CP Ã— 100

Profit = 4/100 Ã— C.P

= Rs. 0.04 x S.P

= C.P + Profit = x + 0.04

x = Rs. 1.04 x

For shirt 2:Profit = 5%:

C.P = Rs. x

Profit = 5/100 Ã— C.P = Rs. 0.05 x

S.P = C.P + Profit = x + 0.05

x = Rs. 1.05 x

It is given that the difference between their profits is Rs. 6

So, 1.05 x âˆ’1.04 x = 6

0.01 x = 6

x = Rs. 600

Thus, C.P = Rs. 600

S.P of shirt 1 = Rs. 1.04 x

= Rs. 1.04 Ã— 600

= Rs. 624

S.P of shirt 2 = Rs.1.05 x

= Rs.1.05 Ã— 600

= Rs. 630.

**PAGE NO 13.12:**

**Question 24:**

**Toshiba bought 100 hens for Rs 8000 and sold 20 of these at a gain of 5%. At what gain percent she must sell the remaining hens so as to gain 20% on the whole?**

**ANSWER:**

C.P of 100 hens = Rs. 8000

Cost of one hen = 8000/100 = Rs. 80

C.P of 20 hens = Rs.( 80 Ã— 20) = Rs. 1600

Gain% = 5%

S.P = C.P

S.P = 1600 Ã— 105/100 = Rs. 1680

C.P of 80 hens = Rs.(80 Ã— 80) = Rs.6400

Gain on 80 hens = S.P of 80 hensâˆ’C.P of 80 hens

Gain on 100 hens = Gain on 80 hens + Gain on 20 hens

Gain on 100 hens = Rs.(80 + S.P of 80 hens âˆ’ 6400)

Gain% on 100 hens =

1600 = 80 + S.P of 80 hens âˆ’ 6400

S.P of 80 hens = Rs.( 1600 + 6400âˆ’80)S.P of 80 hens = Rs. 7920

Gain on 80 hens = S.P of 80 hens âˆ’C.P of 80 hens = Rs.(7920âˆ’6400) = Rs.1520

Gain% on 80 hens = Gain on 80 hens

C.P of 80 hens = 23.75%

Therefore, Toshiba gained 23.75% on 80 hens.