# RD Sharma Solutions Class 8 Profit Loss Discount And Value Added Tax Exercise 13.1

## RD Sharma Solutions Class 8 Chapter 13 Exercise 13.1

#### Exercise 13.1

Question 1: A student buys a pen for Rs 90 and sells it for Rs 100. Find his gain and gain percent.

Solution:

As C.P of pen = Rs.90

and S.P of pen = Rs. 100

Gain = SP-CP

= 100-90

Gain = 10

Gain % = gain * 100

C.P = 10(10090)

Gain % = $11\frac{1}{9}$%

Question 2: Rekha bought a saree for Rs.1240 and sold it for Rs. 1147. Find her loss and loss percent.

Solution

As C.P of saree = Rs. 1240

and S.P of saree = Rs. 1147

Loss = CP-SP

= Rs (1240-1147)

Loss = Rs. 93

Loss% = $\frac{93}{1240}\times 100$

Loss% = 7.5 %

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.

Solution

As C.P of 9 apples = Rs. 9.60

so, CP of 1 apple = $\frac{9.60}{9}=1.06$

and S.P of 11 apple = Rs. 12

so, SP of 1 apple = $\frac{12}{11}=1.09$

Clearly, we can see that

SP of 1 apple > CP of 1 apple

Now, we got profit on selling apples = SP-CP

= 0.022

Gain% = $\frac{0.022}{1.06}\times 100$

= 2.27 %

Question 4: The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percentage.

Solution

Assume the cost price of 1 article be Rs. p

and the selling price of 1 article be Rs. q

Hence, 10p = 9q

1 C= $\frac{9}{10}$q

this shows that the cost price is lesser than the selling price.

Profit = S.P-C.P

= 9S- $\frac{9}{10}$q

= $\frac{81}{10}$q

= 8.1 q

Profit = SP-CP

= $11\frac{1}{9}$%

Question 5: A retailer buys a radio for Rs.225. his overhead expense are Rs15. if he sells the radio for Rs.300, determine the profit percentage.

Solution

As given the cost of Radio = Rs 225

and Overhead expenses = Rs 15

therefore, Total expenses = Rs.(225+15) = Rs.240

S.P = Rs.300

Profit = SP-CP = Rs (300-240) = Rs.60

Profit% = $\frac{60}{240}\times 100$

= 25%

Question 6: A retailer buys a cooler for Rs.1200 and overhead expenses are on it are Rs.40. if he sells the cooler for Rs.1550, Determine the profit percentage.

Solution

As Cooler cost = Rs.1200

So, Total cost = Rs.(1200+40) = Rs.1240

Now, S.P of the cooler = 1550

Profit = S.P-C.P

= Rs.(1550-1240)

= Rs. 310

Profit% = $\frac{310}{1240}\times 100$

= 25%

Question 7: A dealer buys a wrist watch for Rs. 225 and spends Rs.15 on its repairs. If he sells the same for Rs.300, find his profit percentage.

Solution

Total amount the dealer pays for the wrist watch =  Rs.225

The money he spent on repairing the wrist watch = Rs.15

So, Total expenses = Rs.(225+15) = Rs.240

Now, S.P = Rs.300

Profit = SP-CP = Rs (300-240) = Rs.60

Profit% = $\frac{60}{240}\times 100$

= 25%

Question 8

Ramesh bought two boxes for Rs.1300. he sold one box at a profit of 20% and the other at a loss of 12%. If the selling price of both boxes

Solution

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

Hence, the cost of the second box will be Rs.(1300-x)

As profit on the first box = 20%

and the Loss on the second box = 12%

So, S.P of the first box = $\frac{120x}{100}$

= $\frac{6x}{5}$

and S.P of the second box = Rs. 28600 – $\frac{88x}{100}$

= Rs.28600 – $\frac{22x}{25}$

As the S.P of the two boxes are equal. So,

= $\frac{6x}{5}$ = Rs.28600 – $\frac{22x}{25}$

= x = 14300 – $\frac{110x}{260}$

= x= 550

Now the C.P of 1st box is Rs. 550

C.P of the 2nd box = Rs.(1300-550) = Rs. 750

Therefore the C.P of the two boxes are Rs.550 and Rs.750 respectively.

Question 9

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

Solution

Assume the cost price of one pen be Rs. C

Now, the selling price be Rs. S

So, 10S = 14C

C = $\frac{10}{14}S$

But, the C.P is less than the S.P.

Profit = 140-100 and Profit % = 40%

The required profit percentage is 40%.

Question 10

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

Solution

Assume the cost price of one chair be Rs. y

Let S.P be Rs. x

So, 18y = 16x

But, the C.P of the chair is more than that of S.P.

Profit% = $\frac{1800-1600}{18}$

= $\frac{200}{16}$

= 12.5%

So, the required profit %  is 12.5%.

Question 11

If the selling price of 18 oranges is equal to the cost price of 16 oranges , find the gain or loss percentage

Solution

Assume the C.P of one chair be Rs. C

S.P be Rs. S

So, 18C = 16S

But, the C.P of the chair is more than that of S.P.

Profit% = $\frac{1800-1600}{18}$

= $\frac{200}{18}$

= $11\frac{1}{9}$%

Hence the profit percentage is $11\frac{1}{9}$%.

Question 12

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

Solution

Assume the C.P of the motor cycle for Ravish be Rs. y

And Loss % = 28%

Selling Price = $\frac{72y}{100}$

S.P of the motorcycle for Ravish = C.P of the motorcycle for Vineet

Total money Vineet spent on repairs = Rs.1680. So, total c.p of the motorcycle for him =

Rs($\frac{72x}{100}$ + 1680(12.5) + 100(100)

= (35910)(100)(100) = $\frac{72x}{100}$

= 35910000 = 8100x +18900000

= y= 42000

and Ravish paid Rs.42000 for the motorcycle.

Question 13

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

Solution

Aa S.P of the book = Rs. 258

and Gain = 20%

sO, S.P = $\frac{120}{100}\times 258$

= Rs. 215

And C.P = $\frac{130}{100}\times 215$

= Rs. 279.50

Hence, the book seller should keep the S.P of the book as Rs. 279.50 to get 30% profit.

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?

Solution

The cost price of briefcase = Rs. 800

and Loss = 8%

Selling Price = $\frac{92}{100}\times 800$

= Rs. 736

As the price is reduced further by 5 %

So, S.P = $\frac{95}{100}\times 736$  = Rs. 699.20

Hence, the S.P of the briefcase is Rs. 699.20

Question 15

By selling 90 ball pens for Rs160 a person loses 20%. How many ball pens should be sold at Rs.96 so as to have a profit of 20%?

Solution

As selling price of 90 ball pens = Rs 160

and Loss= 20%

Cost Price = $\frac{100}{20}\times 160$

= Rs. 200

As,

Selling price of 90 ball pens = Rs. 96

and Profit = 20%

So, Cost Price = $\frac{100}{120}\times 96$

= Rs .80

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

Hence, Rs.80 is the Costprice of = 90 ($\frac{80}{200}$) =  36 ball pens

Therefore, 36 ball pens must be sold at Rs. 96 to get  a profit of 20%

Question 16

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

Solution

Assume the Cost Price of the article be Rs. x

So, Profit = 25%

and Original S.P = x + $\frac{25}{100}x$

= Rs. $\frac{5x}{4}$

If he gets it at 20% less,

then C.P = x- $\frac{20}{100}$x

= Rs. $\frac{4x}{5}$

He sold the article at Rs. 36.75

Therefore, the S.P = Rs. $\frac{5x}{4}$ – 36.75

As it is given, that he might have gained 30% selling at that price.

Therefore, gain% = S.P-C.P

= $\frac{5x}{4}$ -36.75 – $\frac{4x}{5}$

= $\frac{25x-16x}{20}$ -36.75

So, gain percent = $\frac{9x}{20}$-36.75- $\frac{4x}{5}$(100)

= 18375x = 18375105

= x = 175

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

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 percentage.

Solution

The shopkeeper sells 950 gm pulses and receives a grain of 50 gm.

Then if he sells 10 gm of pulses, he will get profit:

$\frac{50}{950}\times 100$

So, his gain%  is $55\frac{1}{9}$%

Question 18

A dealer bought two tables for Rs.3120. he sold one of them at a loss of 15% and the 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.

Solution

It is given that the S.P is the same for both the tables.

Suppose the C.P of one table be y

Now the C.P of the other table wil be = Rs.3120-y

Loss on the 1st table = 15%

So, S.P = $\frac{85y}{10}$

= 0.85y

Gain on the 2nd table = 36%

136(3120-y)

As both the tables have the similar S.P

2.21y = 4243.20

= y= 1920

The C.P of the table is Rs.1920

The C.P of the other table is Rs.(3120-1920)

= Rs.1200

Question 19

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

Solution

S.P is same for both of the fans. (Given)

As the C.P of the 1st fan be Rs. y

So, C.P of the 2nd fan be Rs. (3605-y)

As the Profit on the 1st fan = 15%

and the loss on the 2nd fan = 6%

For the 1st fan, Selling Price = $\frac{115y}{100}$

= $\frac{23y}{20}$

For the 2nd fan, S.P = $\frac{91y}{100}$

As, S.P of both the fans is exactly the same

= $\frac{23y}{20}$ = 3605 – $\frac{91y}{100}$

= y = 1592

Cost Price of the 1st fan = Rs. 1592

Cost Price of the 2nd fan = Rs.(3605-1592)

= Rs. 2012.50

The C.P of the two of the fans are Rs.1592 and Rs. 2012.50 respectively.

Question 20

Some toffees are bought at a 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 per toffee, find the gain or loss percent on the whole transaction.

Solution

Assume the total number of toffees got be Rs. y

Also, yat the rate of 11 have got for Rs.10,

So, the total money spent on toffees = $\frac{200y}{198}$

= $\frac{100y}{99}$

As it is given that y toffees will be sold at Re.1 per toffee.

So, the S.P of y toffees = Rs. y(1)

As Cost Price is more than Selling Price, it will be a loss.

So, the Loss= C.P-S.P

= $\frac{100x}{99}$ – y

= $\frac{y}{99}$

Loss% = 1%

Therefore, the total loss on the whole transaction will be 1%

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.

Solution

Assume the S.P of the tricycle be Rs. y

and Assume the C.P of the tricycle be Rs. x

As Profit % = 16%

Now we have,

= y= x+ $\frac{16x}{100}$

= y = x+ 0.16x

When S.P is increased by Rs.100, we will get

= y+ 100 = x + $\frac{20x}{100}$

the put y = 1.6x

= 1.16x+100 = x+0.2x

= 1.16x +100 = 1.2x

= x = 2500

The Cost Price of the cycle is 2500

Thus, Cost Price of the tricycle is Rs. 2500.

Question 22

Shabana bought 16 dozens ball pens and sold them at a loss of to S.P of 8 ball pens. Find:

(i) Her loss percent

(ii) P of 1 dozen ball pens, if she purchased these 16 dozens ball pens for Rs.576

Solution

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

Assume S.P of 1 pen be Rs. y

Hence, S.P of 192 pens = 192y

Cost Price of 8 pens = Rs. 8y

S.P of 8 pens is equal to the loss of selling 192 pens. (Given)

So, loss= Rs.8y

Cost Price of 192 pens = Rs 576

Now, Loss = C.P –S.P

= 8x = 576 – $\frac{192y}{200}$

= 576 y = 576200

=y= 2.88

Hence, loss= RS.23.04

Loss% = 4%

(ii) P of 1 pen = Rs.2.88

hence, S.P of 1 dozen pens = 12y = 12(2.88)

= Rs.34.56

Question 23

The difference between two selling pieces of a shirt at a profit of 4 % and 5% is Rs.6. find:

(i) P of the shirt

(ii) The two selling prices of the shirt

Solution

Assume the C.P of two of the shirts be RS. y

And for one shirt profit = 4%

Now, Profit percent = Rs. 0.04y

and S.P = Rs.1.04y

so, For 2 shirt profit will be = 5%

Profit percentage = Rs. 0.05y

Selling Price = Rs.1.05y

The difference between their profits is Rs.6(Given)

Hence, 1.05y-1.04y = 6

= y = Rs.600

So, C.P = Rs.600

Selling Price of one shirt 1 = Rs.1.04y = Rs. 1.04(600)= Rs. 624

Selling Price of one shirt 2 = Rs.1.05y= Rs. 1.05(600)= Rs. 630

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?

Solution

Cost Price of 100 hens = RS. 8000

Cost of 1 hen = $\frac{8000}{100}$

Now, Rs. 80 Cost Price of 20 hens = Rs (80*20) = Rs. 1600

and the Gain = 5%

Selling Price = $\frac{105}{100}\times 1600$

= Rs. 1680

Cost Price of 80 hens = Rs.(80*80) = Rs. 6400

Profit on 80 hens – C.P 80 hens

Profit on 100 hens = gain on 80 hens + gain on 20 hens

= 80+ S.P of 80 hens – 6400

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

S.P of 80 hens = Rs. 7920

Profit on 80 hens = Selling Price of 80 hens – Cost Price of 80 hens

= Rs. (792-6400) = Rs. 1520

Profit % 80 hens = $\frac{1520}{6400}\times 100$

= 23.75%

So, She gained 23.75% on 80 hens.