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QUESTION: 1

A man sells a TV set for Rs. 33000 and makes a profit of 10%. He sells another TV at a loss of 20%. If on the whole, he neither gains nor loses, find the selling price of the second TV set.

Solution:

The profit of 10% amounts to Rs.3000.

This should also be the actual loss on the second TV.

Thus, the actual loss = Rs.3000 (20% of C.P.)

Hence, the CP of the second set = Rs.15000

SP of the second TV set = 15000 – 3000 = 12000

QUESTION: 2

A feeding bottle is sold for Rs. 150. Sales tax accounts for one-fifth of this and profit one-third of the remainder. Find the cost price of the feeding bottle.

Solution:

Sales tax = 150 / 5 = 30

∵ SP contains Rs. 30 component of sales tax.

Of the remainder (150 – 30 = 120) 1/3rd is the profit.

Thus, the profit = 120 / 3 = 40

Hence, Cost price = 120 – 40 = 80

QUESTION: 3

By selling a cap for Rs. 29.75, a man gains 6.25%. What will be the CP of the cap?

Solution:

SP = 106.25% of the CP.

Thus, CP = 29.75/1.0625 = Rs. 28.

QUESTION: 4

E sells a car priced at Rs. 1,80,000. He gives a discount of 5% on the first Rs. 1,00,000 and 12.5% on the remaining Rs. 80,000. His competitor R sells a car on the same market priced at Rs. 1,80,000. If he wants to be competitive what percent discount should R offer on the marked price.

Solution:

The total discount offered by E = 5% on 1,00,000 + 12.5% on 80,000 = 5,000 + 10,000 = 15,000.

If R wants to be as competitive, he should also offer a discount of Rs. 15,000 on 1,80,000.

Discount percentage = (15000/180000) x 100= 8.33% discount.

QUESTION: 5

A man sells an article at 10% above its cost price. If he had bought it at 15% less than what he paid for it and sold it for Rs. 33 less, he would have gained 10%. Find the cost price of the article.

Solution:

S.P. at 10% profit = Rs.(110y/100) = 11y/10

New C.P. of article = 85y/100 = 17y/20

S.P. = Rs.(17y/20 * 110/100)

New S.P. of article = Rs. 187/200

**According to Question,**

11y/10 - 187y/200 = 33

33y/200 = 33

y = 200

QUESTION: 6

E owns a house worth Rs. 20,000. He sells it to R at a profit of 25%. After some time, R sells it back to E at 25% loss. Find E’s loss or gain per cent.

Solution:

CP = 20000

Profit = 25/100 of 20000 = 5000

SP = Profit + CP = 25000

__New transaction__

CP= 25000

Loss = 25% of 25000 = 6250

SP = CP - Loss = 18750

P's gain = 1250

TOTAL gain = 6250

Total gain % = 6250/20000 × 100 = 625/20 = 31.25%

QUESTION: 7

A machine costs Rs. 1025. If it is sold at a loss of 25%, what will be its cost price as a percentage of its selling price?

Solution:

A loss of 25% means a cost price of 100 corresponding to a selling price of 75. CP as a percentage of the SP would then be 133.33%

**Alternatively,**

Cost price = 1025

Loss% = 25%

SP = 1025 - (1025 * 25/100) = 768.75

⇒ 768.75 * (x/100) = 1025

⇒ 768.75x = 102500

⇒ x = 102500/768.75 = 133.33%

QUESTION: 8

E sold at table to R at a profit of 25%.R sold the same table to S for Rs. 90 thereby making a profit of 20%. Find the price at which E bought the table from Z if it is known that Z gained 25% in the transaction.

Solution:

R sold the table at 20% profit at Rs. 90. Thus R's cost price x 1.2 = 90

R’s Cost price = Rs. 75

We also know that E sold it to R at 25% profit.

Thus, E’s Cost price x 1.25 = 75

⇒ E’s cost price = 60

QUESTION: 9

125 toffees cost Rs. 75. Find the cost of one million toffees if there is a discount of 40% on the selling price for this quantity.

Solution:

The cost per toffee = 75 / 125 = Rs. 0.6 = 60 paise.

Cost of 1 million toffees = 600000.

∵ There is a discount of 40% offered on this quantity.

Thus, the total cost for 1 million toffees is 60% of 600000 = 360000

QUESTION: 10

A dishonest dealer marks up the price of his goods by 20% and gives a discount of 10% to the cus- tomer. Besides, he also cheats both his supplier and his buyer by 100 grams while buying or selling 1 kilogram. Find the percentage profit earned by the shopkeeper.

Solution:

**While buying**, he buys 1100 grams instead of 1000 grams (due to his cheating).

Suppose he bought 1100 grams for Rs. 1000

**While selling**, he sells only 900 grams when he takes the money for 1 kg.

**According to the problems**

He sells at 8% profit (20% markup and 10% discount).

Hence his selling price is Rs. 1080 for 900 grams.

To calculate profit percentage, we either equate the goods or the money.

In this case, let us equate the money as follows:

**Buying:**1100 grams for Rs. 1000

Hence 1188 grams for Rs. 1080

**Selling**: 900 grams for Rs. 1080

Hence, profit% = 288/900 = 32%

(using goods left by goods sold formula)

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