#### 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:**

C.P of pen = Rs.90

S.P of pen = Rs. 100

Gain = SP-CP

= 100-90 = 10

Gain % = gain * 100

C.P = 10(10090)

= \(11\frac{1}{9}\)

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

**Solution**

C.P of saree = Rs. 1240

S.P of saree = Rs. 1147

Loss = CP-SP

= Rs (1240-1147)

= Rs. 93

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

= 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**

C.P of 9 apples = Rs. 9.60

CP of 1 apple = \(\frac{9.60}{9}=1.06\)

S.P of 11 apple = Rs. 12

SP of 1 apple = \(\frac{12}{11}=1.09\)

Clearly,

SP of 1 apple > CP of 1 apple

We get 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**

Let the cost price of 1 article be Rs. C

Let the selling price of 1 article be Rs. S

Therefore, 10C = 9S

1 C= \(\frac{9}{10}\)

So the cost price is less than the selling price.

Profit = S.P-C.P

= 9S- \(\frac{9}{10}\)

= \(\frac{81}{10}\)

= 8.1 S

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**

Radio cost = Rs 225

Overhead expenses = Rs 15

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**

Cooler cost = Rs.1200

Overhead cost = Rs.40

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

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**

A dealer buys a wrist watch for Rs.225

Money spent on repairing the watch = Rs.15

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 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**

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%

S.P of the first box = \(\frac{120x}{100}\)

= \(\frac{6x}{5}\)

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

= Rs.28600 – \(\frac{22x}{25}\)

Selling prices of both of the boxes are equal. So,

= \(\frac{6x}{5}\)

= x = 14300 – \(\frac{110x}{260}\)

= x= 550

The cost price of first box is Rs. 550

Cost price of the second box = Rs.(1300-550)

= Rs. 750

The cost prices of the 2 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**

Let the cost price of one pen be Rs. C

The selling price be Rs. S

Therefore, 10S = 14C

C = \(\frac{10}{14}S\)

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

Profit = 140-100

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**

Let the cost price of one chair be Rs. C

Selling price be Rs. S

Therefore, 18C = 16S

However, the cost price of the chair is more than that of selling price.

Profit% = \(\frac{1800-1600}{18}\)

= \(\frac{200}{16}\)

= 12.5%

The required profit percent 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**

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

Selling price be Rs. S

Therefore, 18C = 16S

However, the cost price of the chair is more than that of selling price.

Profit% = \(\frac{1800-1600}{18}\)

= \(\frac{200}{18}\)

= \(11\frac{1}{9}\)

The profit % 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**

Let the cost price of the motor cycle for Ravish be Rs. x

Loss % = 28%

S.P = \(\frac{72x}{100}\)

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(\(\frac{72x}{100}\)

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

= 35910000 = 8100x +18900000

= x= 42000

Ravish bought the motorcycle for Rs.42000

**Question 13**

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

**Solution**

Selling price of the book = Rs. 258

Gain = 20%

S.P = \(\frac{120}{100}\times 258\)

= Rs. 215

C.P = \(\frac{130}{100}\times 215\)

= Rs. 279.50

Therefore, the book seller must sell the book at Rs. 279.50 to make 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**

C.P of the briefcase = Rs. 800

Loss = 8%

S.P = \(\frac{92}{100}\times 800\)

= Rs. 736

The price is decreased further by 5 %

S.P = \(\frac{95}{100}\times 736\)

= Rs. 699.20

The selling price 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**

S.P of 90 ball pens = Rs 160

Loss= 20%

C.P = \(\frac{100}{20}\times 160\)

= Rs. 200

Now,

S.P of 90 ball pens = Rs. 96

Profit = 20%

C.P = \(\frac{100}{120}\times 96\)

= Rs .80

Rs .200 is the cost price of 90 ball pens.

Therefore, Rs.80 is the C.P of = 90 (\(\frac{80}{200}\)

Thus, 36 ball pens should be sold at Rs. 96 to earn 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**

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

Profit = 25%

Original S.P = x + \(\frac{25}{100}x\)

= Rs. \(\frac{5x}{4}\)

If he purchased it at 20% less,

C.P = x- \(\frac{20}{100}\)

= Rs. \(\frac{4x}{5}\)

He sold the article at Rs. 36.75

So, the selling price = Rs. \(\frac{5x}{4}\)

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

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

= \(\frac{5x}{4}\)

= \(\frac{25x-16x}{20}\)

So, gain % = \(\frac{9x}{20}\)

= 18375x = 18375105

= x = 175

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**

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

If he sells 10 gm of pulses, he will gain:

\(\frac{50}{950}\times 100\)

His gain percentage 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**

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

Let the C.P of 1 table be x

Then the C.P of the other table be = Rs.3120-x

Loss on the first table = 15%

Therefore, S.P = \(\frac{85x}{10}\)

= 0.85x

Gain on the second table = 36%

136(3120-x)

Since both the tables have the same S.P

2.21x = 4243.20

= x= 1920

The cost price of the table is Rs.1920

The cost price 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**

It is given that the S.P is same for both of the fans.

Let the C.P of the first fan be Rs. x

Therefore, C.P of the second fan be Rs. (3605-x)

Profit on the first fan = 15%

Loss on the second fan = 6%

For the first fan, S.P = \(\frac{115x}{100}\)

= \(\frac{23x}{20}\)

For the second fan, S.P = \(\frac{91x}{100}\)

Since, S.P of both the fans is the same

= \(\frac{23x}{20}\)

= x = 1592

C.P of the first fan = Rs. 1592

C.P of the second fan = Rs.(3605-1592)

= Rs. 2012.50

The cost prices of the both 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**

Let the total number of toffees bought be Rs. x

Let x_{2 }at the rate of 11 are bought for Rs.10,

Total money spent on toffees = \(\frac{200x}{198}\)

= \(\frac{100x}{99}\)

It is given that x toffees are sold at Re.1 per toffee.

Therefore, the selling price of x toffees = Rs. x(1)

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

Loss= C.P-S.P

= \(\frac{100x}{99}\)

= \(\frac{x}{99}\)

Loss% = 1%

The total loss on the whole transaction would 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**

Let the S.P of the tricycle be Rs. x

Let the C.P of the tricycle be Rs. y

Gain % = 16%

Then we have,

= x= y+ \(\frac{16y}{100}\)

= x = y+ 0.16y

When S.P increases by Rs.100, we get

= x+ 100 = y + \(\frac{20y}{100}\)

Putting x = 1.6y

= 1.16y+100 = y+0.2y

= 1.16y +100 = 1.2y

= y = 2500

The C.P of the cycle is 2500

Thus, C.P 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

Let S.P of one pen be Rs. x

Therefore, S.P of 192 pens = 192x

C.P of 8 pens = Rs. 8x

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

Therefore, loss= Rs.8x

C.P of 192 pens = Rs 576

Loss = C.P –S.P

= 8x = 576 – \(\frac{192x}{200}\)

= 576 x = 576200

=x= 2.88

Therefore, loss= RS.23.04

Loss% = 4%

(ii) P of 1 pen = Rs.2.88

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

Let the C.P of both the shirt be RS. X

For 1 shirt profit = 4%

Profit% = Rs. 0.04x

S.P = Rs.1.04x

For 2 shirt profit = 5%

Profit% = Rs. 0.05x

S.P = Rs.1.05x

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

So, 1.05x-1.04x = 6

= x = Rs.600

Thus, C.P = Rs.600

S.P of 1 shirt 1 = Rs.1.04x = Rs. 1.04(600)= Rs. 624

S.P of 1 shirt 2 = Rs.1.05x = 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**

C.P of 100 hens = RS. 8000

Cost of one hen = \(\frac{8000}{100}\)

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

Gain = 5%

S.P = \(\frac{105}{100}\times 1600\)

= Rs. 1680

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

Gain on 80 hens – C.P 80 hens

Gain 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

Gain on 80 hens = S.P of 80 hens – C.P of 80 hens

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

Gain % 80 hens = \(\frac{1520}{6400}\times 100\)

= 23.75%

Therefore, Toshiba gained 23.75% on 80 hens.