Chapter 13 - Proft, Loss, Discount and Value Added Tax (VAT) (Part -1), Class8 RD Sharma Solutions | RD Sharma Solutions for Class 8 Mathematics PDF Download

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 −CP

Gain = 100−90 = 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 = CP−SP

Loss =  Rs.(1240−1147) = 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

∴ C.P of 1 apple = Rs 9.609 = Rs16/15

S.P of 11 apples  =  Rs 12

∴ 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

00/9−100 = 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 = SP−CP         

=  Rs. (300−240)         

= Rs. 60

Profit% = Profit/C.P × 100

= 60/240 × 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 = SP−CP         

= Rs. (1550−1240)         

= Rs. 310

Profit% = Profit/C.P × 100

= 310/1240 × 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 = SP−CP         

= Rs. (300−240)         

= Rs. 60

Profit% = Profit/C.P × 100

= 60/240 × 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. (1300− 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 = 143000−110 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.(1300−550) = 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%

140−100 = 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%

180016−100 = 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 = 100−loss%

Loss% = 100−1600/18

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

⇒ 35910 × 100 × 100 = (72 x + 168000)(112.5)

⇒ 359100000 = 8100 x + 18900000

⇒ 340200000 = 8100 x

⇒ 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 × 0.92

= Rs. 736

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

=  Rs.(736−736 × 5/100) 

= 736 × 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 −20/100.x

= Rs. 4x/5

He sold the article at Rs 36.75 less.

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

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

Therefore, gain% =

S.P−C.P = 5x/4−36.75−4 x 5

= 5x/4−4x/5−36.75

−36.75

= 9x/20−36.75

So, gain% =

225 x −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 × 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.(3120− 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(3120− x )

Since both tables have the same S.P,

So, 0.85 x = 1.36(3120− x )

0.85 x = 4243.20−1.36 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. ( 3120−1920) = 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. (3605− 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

= (3605− x )(91/100)

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

2300 x = 91(72/100−20 x )2300

x = 6561100−1820 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. (3605−1592.50)             = 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 × 1 = Rs.  x

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

Loss = C.P−S.P

= x/99

Loss% = Loss/C.P × 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

⇒ x + 100 = y +

Putting  x = 1.6y, we get

⇒ 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 × 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.P−S.P

8 x = 576−192 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 × 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 × 100

Profit = 4/100 × 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 × 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 −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 × 600

= Rs. 624

S.P of shirt 2 =  Rs.1.05 x

=  Rs.1.05 × 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 × 20) = Rs. 1600

Gain% = 5%

S.P = C.P

S.P = 1600 × 105/100 = Rs. 1680

C.P of 80 hens = Rs.(80 × 80) = Rs.6400

Gain on 80 hens = S.P of 80 hens−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 − 6400)

Gain% on 100 hens =  

1600 = 80 + S.P of 80 hens − 6400

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

Gain on 80 hens =  S.P of 80 hens −C.P of 80 hens = Rs.(7920−6400) = 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.