## RD Sharma Solutions Class 8 Chapter 13 Exercise 13.1

#### Exercise 13.1

**Question 1:Â ****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

**GainÂ **= 10

Gain % = gain * 100

C.P = 10(10090)

**Gain %** = \(11\frac{1}{9}\)%

**Question 2:Â ****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)

**LossÂ **= Rs. 93

**Loss%** = \(\frac{93}{1240}\times 100\)

**Loss%** = 7.5 %

**Question 3:Â ****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:Â ****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:Â ****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:Â ****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

and Overhead cost = Rs.40

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:Â ****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 =Â 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 boxesÂ **

**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 profitÂ % Â 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 itâ€™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 paidÂ 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 = \(\frac{95}{100}\times 736\)Â Â = 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 (\(\frac{80}{200}\)) =Â 36 ball pens

Therefore, 36 ball pens must be sold at Rs. 96 to getÂ 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. \(\frac{5x}{4}\) â€“ 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%Â 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, y_{2Â }at 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

= \(\frac{100x}{99}\) â€“ 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**

**SolutionÂ Â **

(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 â€“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 â€“ C.P 80 hens

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

= 80+ S.P of 80 hens â€“ 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 â€“ 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.