#### Exercise 13.2

Question 1:Â Find the S.P.

Solution:

(i) P= Rs.13000 and Discount= 10%

We know that S.P = M.P â€“ discount

Discount% = \(\frac{discount}{MP}\times 100\)

= \(\frac{10}{1300}\times 100\)

= Rs.130

S.P = Rs (1300-130) = Rs. 1170

(ii) Â M.P= Rs.500 and Discount= 15%

We know that S.P = M.P â€“ discount

Discount% = \(\frac{discount}{MP}\times 100\)

= \(\frac{15}{100}\times 500\)

= Rs.75

S.P = Rs.(500-75) =Rs. 425

Question 2:Â Find the M.P.

Solution

(i) P= Rs.1222 and Discount= 6%

Given, S.P = Rs. 1222

Discount = 6%

M.P = \(100\times \frac{S.P}{100}-discount\)

= \(100\times \frac{1222}{100}-6\)

= Rs.1300

(ii) P= Rs.495 and Discount= 1%

Given, S.P = Rs. 495

Discount = 1%

M.P = \(100\times \frac{S.P}{100}-discount\)

= \(100\times \frac{495}{100}-1\)

= Rs.500

Â

Question 3:Â Find the discount in percent.

Solution

(i) P= Rs.900 and S.P =Rs.873

We know that,

S.P = M.P- discount

= 873 = 900- discount

= discount = (900-873) = Rs. 27

Discount% = \(100\times \frac{discount}{M.P}\)

= \(100\times \frac{27}{900}\)

= 3%

(ii) P= Rs.500 and S.P =Rs.425

We know that,

S.P = M.P- discount

= 425 = 500- discount

= discount = (500-425) = Rs. 75

Discount% = \(100\times \frac{discount}{M.P}\)

= \(100\times \frac{75}{500}\)

Question 4Â A shop selling sewing machines offers 3% discount on all cash purchases. What cash amount does a customer pay for a sewing machine the price of which is marked as Rs.650?

Solution

Discount = 3%

Marked price = Rs.650

Now, 3% of the M.P = \(\frac{3}{100}\times 650\)

= Rs.19.50

So, M.P = M.P â€“ discount

= 650 â€“ 19.50

= Rs.630.50

Question 5:Â The marked price of a ceiling fan is Rs. 720. During off-season, it is sold for Rs.684, determine the discount percentage.

Solution

Given, M.P of the ceiling fan = Rs. 720

S.P of the ceiling fan = Rs. 684

Since S.P = M.P â€“ discount

Discount = M.P â€“S.P

= Rs.(720-684)

= Rs. 36

Discount% = \(\frac{discount}{MP}\times 100\)

= \(\frac{36}{720}\times 100\)

= 5%

Question 6

On the eve of Gandhi Jayanti, a saree is sold for Rs.720 after allowing 20% discount. What is the market price?

Solution

Given, S.P of the saree = Rs. 720

Discount on the saree = 20%

We know, Discount% = \(\frac{discount}{MP}\times 100\)

Let the M.P of the saree be Rs. x.

Therefore, discount = \(\frac{20x}{100}\times 720 \)

Since, S.P = M.P – discount

= 720 = x- 0.20(720)

= x= Rs. 900

Thus, the M.P of the saree is Rs.900

Â Question 7

After allowing a discount of \(7\frac{1}{2}\)

Solution

Given, S.P of the article = Rs. 555

Discount = 7.5%

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

Therefore, Discount% = \(\frac{MP}{100}\times discount\)

= Rs.Â 0.075 x

Since, S.P = M.P â€“ discount

= 555 = x- 0.075x

= x = Rs. 600

Thus, the M.P of the article is Rs.600

Question 8

A shopkeeper allows his customers 10% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked Rs.250?

Solution

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

M.P of the article = Rs.250

Discount = 10%

Discount = 10% of 250

= \(\frac{10}{100}\times 250\)

= Rs.25

S.P = M.P â€“discount

= Rs.( 250-25)

= Rs.225

Profit = 25%

C.P = \(\frac{100}{100+25}\times 225\)

= Rs.180

The C.P of the article is Rs. 180

Â Question 9

A shopkeeper allows 20% off on the marked price of goods and still gets a profit of 25%. What is the actual cost to him of an article marked as Rs.500?

Solution

Given,

M.P of the an article = Rs.500

Discount = 20%

Therefore, discount = 20% of 500

= \(\frac{20}{100}\times 500\)

= Rs. 100

S.P = M.P â€“ discount

Discount = (M.P â€“S.P)

= Rs. (500-100)

= Rs. 400

Profit % = 25%

C.P = \(\frac{100}{100+25}\times 320\)

= Rs. 320

The actual cost price of the article is Rs.320.

Question 10

A tradesman marks his goods at such a price that after allowing a discount of 15%, he makes a profit of 20%.Â What is the marked price of an article whose cost price is Rs.170?

Solution

Given,

C.P of the article =Rs. 170

Profit = 20%

We know that, S.P = \(\frac{120}{100}\times 170\)

= Rs. 204

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

Discount = 15%

Therefore, discount = 15% of x

= \(\frac{15}{100}\times x\)

= 0.15x

M.P = S.P + discount

M.P = Rs. 240

The marked price of the article is Rs.240.

Question 11

A shopkeeper marks his goods at such a price that after allowing a discount of 25% on the marked price , he still makes a profit of 50%. Find the ratio of the C.P to the M.P

Solution

Let the C.P be Rs. x

Let the M.P be Rs. y

Gain % = 50%

S.P = \(\frac{100}{100+50}\times x\)

=32x

Discount = 25%

Discount = 25% of y

= \(\frac{25}{100}\times y\)

= Rs. 0.25y

S.P = M.P â€“ discount

= y- 0.25y

= 0.75 y

Also, S.P = 32x

Comparing both the values for S.P we get,

32x = \(\frac{0.75y}{xy}\)

C.P: M.P = 1:2

Question 12

A cycle dealer offers a discount of10% and still makes a profit of 26%. What is the actual cost to him of a cycle whose marked price is Rs.840?

Solution

Given,

M.P of the cycle = Rs.840

Discount = 10%

So, S.P = M.P â€“discount

= 840 – \(\frac{10}{100}\)

= Rs. 756

S.P = Rs.756

Gain = 26%

C.P = \(\frac{100}{100+26}\times 756\)

=Â \(\frac{100}{126}\times 756\)

= Rs. 600

Hence, the C.P of the cycle is Rs. 600

Â Question 13

A shopkeeper allows 23% on commission on his advertised price and still makes a profit of 10%. If he gains Rs.56 on one item, find his advertised price.

Solution

Let the C.P of the item be = Rs .x

Profit% = 10%

Profit = 10% 0f x

= \(\frac{110x}{100}\)

= Rs. 1.1x

Again, Profit = S.P â€“ C.P

= Rs. (1.1x-x) = Rs. 0.1x

We get,

= 0.1x = 56

= x= Rs.560

The advertised price = Rs.800

The advertised price of the item is Rs. 800

Â Question 14

A shopkeeper marks his goods at 40% above the cost price but allows a discount of 5% for cash payment to his customers. What actual profit does he make, if he receives Rs.1064 after paying the discount?

Solution

Let the original cost price of the item be Rs. x

Profit = 40%

Profit = \(\frac{40}{100}\)

M.P = x+ 0.40x=1.4x

Discount = M.P â€“ S.P

= Rs. 800.

Profit = Rs.(1064-800)

=Rs. 264

The actual profit by the shopkeeper is Rs. 264

Â Question 15

By selling a pair of earrings at a discount of 25% on the marked price, a jeweler makes a profit of 16%.if the profit is Rs.48, what is the cost price? What is the marked price and the price at which the pair was eventually bought?

Solution

Let the cost price of the pair of the earrings be Rs. x

Profit = 16%

S.P = \(\frac{116}{100}\times S.P\)

Profit = S.P â€“ C.P

= \(\frac{116}{100}\times S.P\)

16x = 4800

=x = 300

\(\frac{116x}{100}= 348\)

Discount = \(\frac{34800}{75}\)

= Rs. 464

Thus, C.P of the pair of earrings = Rs. x = Rs. 300

S.P of the pair of earrings = Rs. 348

M.P of the pair of earrings = Rs. 464

Â Question 16

A publisher gives 32% discount on the printed price of a book to booksellers. What does a bookseller pay for a book whose printed price is Rs.275?

Solution

Discount allowed by the publisher =- 32% on the printed price

Printed price = Rs. 275

So, 32% of Rs. 275

= \(\frac{32}{100}\times Rs.275\)

= Rs. 88

The bookseller pays = Rs.275 â€“ Rs. 88

= Rs. 187

The bookseller pays Rs. 187 for a book.

Question 17

After allowing a discount of 20% on the marked price of a lamp, a trader loses 10%.By what percentage is the marked price above the cost price?

Solution

Let the C.P of the lamp be RS. 100

Loss= 10% of C.P

S.P = C.P â€“ loss

= Rs.100 â€“ Rs. 10

= RS. 90

The trader allows a discount of 20%

This means when the M.P is Rs. 100, the S.P will be Rs. 80

Now, Rs. 80 is the S.P, the M.P = Rs. 100

If Re.1 is the S.P, then M.P = Rs. \(\frac{100}{80}\)

Rs. 90 is the S.P then, M.P = Rs. \(\frac{100}{80}\times 90\)

= Rs. 112.50

Hence, the trader marks his goods at 12.5% above the cost price.

Â Question 18

The list price of a table fan is Rs.480 and it is available to a retailer at 25% discount. For how much should a retailer sell it to gain 15%?

Solution

Marked price of the table= Rs. 480

Discount = 25%

Therefore, cost price = 25% of Rs. 480

= \(\frac{125}{100}\times 480\)

= Rs. 360

It is given that the profit on the table fan is 15%

Gain = Rs. 54

S.P = Rs. 364 + Rs. 54

= Rs. 414

Thus, the retailer will sell the table fan for Rs. 414

Â Question 19

Rohit buys an item at 25% discount on the marked price. He sells it for Rs.660, making a profit of 10%. What is the marked price of the item?

Solution

Given, S.P of the item = Rs. 660

Discount on the item = 25%

Profit on the item = 10%

Discount = 25% of S.P

Discount = \(\frac{660}{100-25}\times 100\)

= Rs. 880

Thus, the marked price of the item is Rs. 880

Question 20

A cycle merchant allows 20% discount on the marked price of the cycles and still makes a profit of 20%. If he gains Rs.360 over the sale of one cycle, find the marked price of the cycle?

Solution

Given, gain on one cycle = Rs. 360

Gain = 20%

S.P = \(\frac{120}{100}\times 1800\)

= Rs. 2160

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

M.P = \(\frac{2160}{80}\times 10\)

= Rs. 2700

Hence, the M.P of one cycle is Rs. 2700

Question 21

Jyoti and Meena run a ready â€“ made garment shop. They mark the garments at such a price that even after allowing a discount of 12.5%, they make a profit of 10%. Find the marked price of a suit which costs them Rs.1470.

Solution

Given, C.P of the suit = Rs 1470

Gain = 10%

S.P = 100 + \(\frac{Gain}{100}\times C.P\)

= 100+ \(\frac{10}{100}\times 1470\)

= Rs. 1617

Discount = 12.5%

So, M.P = \(\frac{S.P}{100}\times 100\)

= \(\frac{1617}{100}\times 100\)

= Rs. 1848

Therefore, the marked price of the suit is Rs. 1848.

Â Question 22

What price should Aslam mark on a pair of shoes which costs him Rs.1200 so as to gain 12% after allowing a discount of 16%?

Solution

Given, C.P of the pair of shoes = Rs. 1470

Gain = 12%

Discount = 16%

So, S.P = \(\frac{Gain}{100}\times C.P\)

= Rs. \(\frac{12}{100}\times 1470\)

= Rs. 1344

Now, the S.P of the pair of shoes = Rs. 1344

Discount = 16%

So, M.P = \(\frac{1344}{100}\times 100\)

= Rs. 1600

Aslam should sell the pair of shoes for Rs. 1600

Â Question 23

Jasmine allows 4% discount on the marked price of her goods and still earns a profit of 20%. What is the cost price of a shirt for her marked as Rs.850?

Solution

Given,

M.P of the shirt = Rs.850

Discount = 4%

Discount allowed =Â \(\frac{4}{100}\times 850\)

= Rs. 34

Thus, the S.P of the shirt = Rs.850 â€“ Rs.34

= Rs. 816

Profit earned by jasmine = 20%

Thus, C.P =Â \(\frac{S.P}{100}\times 100\)

=Â \(\frac{816}{100}\times 100\)

= Rs. 680

Thus, the cost price of the shirt is Rs. 680

Â Question 24

A shopkeeper offers 10% off-season discount to the customers and still makes a profit of 26%. What is the cost price for the shopkeeper on a pair of shoes marked at Rs.1120?

Solution

Given,

M.P of the pair of shoes = Rs. 1120

Discount = 10%

So, S.P = \(\frac{M.P}{100}\)

= \(\frac{90}{100}\times 1120\)

= Rs. 1008

Therefore, C.P = \(\frac{S.P}{100}\times 100\)

= \(\frac{1008}{100}\times 10\)

= Rs. 800

The cost price of the pair of shoes will be Rs. 800

Question 25

A lady shopkeeper allows her customers 10% discount on the marked price of the goods and still gets a profit of 25%. What is the cost price of a fan for her marked at Rs.1250?

Â Solution

Given,

M.P of the fan = Rs. 1250

Discount = 10%

So, discount = 10% of 1250

= \(\frac{10}{100}\times 1250\)

= Rs. 125

Since, S.P = M.P â€“ discount

= Rs.1250- Rs. 125

= Rs. 1125

S.P of the fan = Rs. 1125

Profit % = 25%

C.P = \(\frac{100}{100+25}\times 1125\)

=Â \(\frac{100}{125}\times 1125\)

= Rs. 900

Thus the cost price of the fan is Rs. 900