QUESTIONS ON PROFIT & LOSS (PART-II)

QUERY 11

By selling an umbrella for Rs. 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% on the marked price. He gains during the sale season is?

A) 5%
B) 10%
C) 8%
D) 6.5%

RONNIE BANSAL
Here we need to understand that the umbrella is sold at the marked price itself i.e. Rs 30; and the discount of 10% is allowed after the sale has been made on this price.

Thus the cost price = (100*30)/120 = 25
Now the discount = 10% of 30 = 3
So the resultant sale price = 30 – 3 = 27

Therefore the gain on one umbrella = Resultant Sale Price — Cost Price = 27 – 25 = Rs 2

But we need to calculate it in percentage as the gain in the sale season is asked
So in percentage the gain is = (2*100) /25 = 8% (option ‘C’)

QUERY 12

The cash down value of an article is 12500. It can be brought at credit 14300 payable one year hence at 10% per annum. The trader gets a profit of?

A) 300
B) 400
C) 500
D) 250

RONNIE BANSAL
If 10% for 1 year on the amount (principal + interest) 14300; then the principal = (100/110)*14300 = 13000
Means the sum of Rs 12500 was given on simple interest considering it as Rs 13000
So the profit of the trader = 13000 – 12500 = 500 (option ‘C’)

NOTE: You must remember that the interest got is not a part of profit, rather it’s compensation for the time that one waits to get his principal back.

QUERY 13

A shopkeeper sells a transistor at 15% above its cost price. If he had bought it at 5% more than what he paid for it and sold it for Rs 6 more, he would have gained 10%. The cost price of the transistor is?

A) Rs 1200
B) Rs 1175
C) Rs 1350
D) Rs 1300

MAHA GUPTA
Let the cost price (CP) of the transistor = x
Therefore the first selling price (SP) = 115% of x = 23x/20
And the second CP= 105% of x = 21x/20
And second SP = 110% of 21x/20 = 231x/200

Therefore second SP – first SP = 6
=> 231x/200 – 23x/20 = 6
=> x = 1200
Hence the cost price of the transistor = Rs 1200 (option ‘A’)

QUERY 14

A shopkeeper gives 2 items free for every 3 items purchased. In effect what discount is being offered ?

A) 30%
B) 35%
C) 40%
D) 45%

RONNIE BANSAL
Total items to be got by the buyer = number of free items + number of items intended to be purched
=> 2 + 3 = 5
So discount is 2 on 5; means (2*100)/5 = 40% (option ‘C’)

QUERY 15

A dishonest milkman professes to sell his milk at cost price but he mixes water with it and thereby gains 25%. Percentage of water in the mixture is ?

A) 25%
B) 22%
C) 20%
D) 18%

MAHA GUPTA
Let the C.P. of 100 ltr of MILK is Rs 100
Therefore the SP also of 100 ltr MIXTURE (milk+water) will be Rs 100, where gain is 25%

So the C.P. of 100 ltr of mixture = (100/125)*100 = 80
Hence the gain = 100 – 80 = 20
Obviously this gain is on 100
So the gain in percentage = 20%

But here the gain is only in the form of mix of water in the milk
Hence the percentage of water in the milk = 20% (option ‘C’)

QUERY 16

A man sold a horse at 10% profit. Had he bought it at 20% less and sold for Rs 10 more, he would have made a profit of 40%. What is the cost price of the horse?

A) 400
B) 500
C) 600
D) 1000

MAHA GUPTA
Better to avoid algebraic method as far as possible as it consumes more time. In an objective exam Maths is done best when done orally as far as possible. This solution may be helpful in that:

Let the cost price = 100
Then 1st selling price = 110 (Profit 10%)

The second cost price = 80 (he buys it at 20% less)
The second selling price = 80 + 40% of 80 = 112

Therefore the difference in selling prices = 2
But the actual difference is 10 (5 times of above)

So the cost price = 5*100 = 500 (option ‘B’)

QUERY 17

A dealer buys an article for Rs 380. At what price must the dealer mark it so that after allowing a discount of 5% he still makes a profit of 25 %?

A) 500
B) 400
C) 300
D) 600

MAHA GUPTA
Unless otherwise stated, the profit always is on the cost price. Here the cost price is 380 and the profit is 25%. Hence the profit = 25% of 380 = 95

Hence the selling price = 380 + 95 = 475, obviously it’s after 5% discount on the marked price.

Now let the marked price = 100
So the selling price = 100 – 5% 0f 100 = 95

Hence the price to be marked = (100/95)*475 = 500 (option ‘A’)

QUERY 18

A vendor bought toffees at 5 for a rupee. How many for a rupee must he sell to gain 25%?

A) 3
B) 4
C) 5
D) 6

MAHA GUPTA
Avoid using ‘x’ method as far as possible as it’s more time consuming.

Here the buying price and the selling price remain to be the same. This sum can easily be solved by the options. As the gain is 25% we have to find just which figure when 25% of it added to that gives 5. Obviously it’s 4 (option ‘B’)

Alternate method
Unless otherwise stated the gain is considered to be on the cost price. Find cost price of 1 toffee; which is obviously Re 1/5 = 20 paise.

Gain is 25%, therefore the selling price of 1 toffee = (20 + 20/4) = 25 paise. Hence at this price the vendor needs to sell 4 toffees for a rupee. (option ‘B’)

QUERY 19

A seller uses 920 gm in place of 1 kg to sell his goods. When he sells his articles at 15% gain on CP, the actual percentage of profit is?

A) 25%
B) 30%
C) 20%
D) 15%

MAHA GUPTA
Suppose the seller buys 1 kg of articles for Rs 100; means Rs 100 is the CP. Now he sells his articles at 15% gain on CP; means he earns Rs 15. But also he saves 1 kg – 920 gm = 80 gm of those articles while selling. So his total gain will be Rs 15+the CP of 80 gm.

If CP of 1 kg, i.e. 1000 gm is Rs 100
The CP of 80 gm will be Rs 8

Therefore his total gain = 15+8 = 23

As the seller uses 920 gm in place of 1 kg, so it’s a must to know the CP of 920 gm to know the actual percentage of profit. If the CP of 1000 gm is Rs 100, it will be Rs 92 for 920 gm.

So, now just calculate ‘how much percentage is 23 of 92’ to know the actual percentage of profit.

So the actual percentage of profit is (²³⁄₉₂)*100 = 25 (option ‘A’)

QUERY 20

A cycle agent buys 30 bicycles, of which 8 are first grade and the rest are second grade for Rs 31350. Find at what price he must sell the first grade bicycle so that if he sells the second grade bicycles at 3 quarters of this price, he may make a profit of 40 percent on his outlay.

A) Rs 1791.60
B) Rs 1600
C) Rs 1600.80
D) Rs 1700

MAHA GUPTA
Number of second grade bicycles = 30 – 8 = 22

Because the cost price is Rs 31,350 and the agent makes a profit of 40% on his outlay, his total selling price = 31,350 × ¹⁴⁰⁄₁₀₀ = 43,890
Now, let the selling price of one first grade bicycle = x
Therefore, the selling price of one second grade bicycle = ^3x⁄₄

Now according to above 8x + 22(^3x⁄₄) = 43,890

=> x = 1791.60 (appox)
So he must sell one first grade bicycle for Rs 1791.60 (appox) [option ‘A’)