QUESTIONS ON PROFIT & LOSS (PART-V)

QUERY 41

The price of stone of weight 2 kg is Rs 40,000. This stone falls and breaks in ratio 3 : 2. What is the loss when price varies with square of weight?

A) Rs 18,000
B) Rs 18,600
C) Rs 19,200
D) Rs 19,700

MAHA GUPTA
As the price varies with square of weight, there must be a constant part of price.

Now let that constant part of price = Rs x
So we can say 2²x = 40,000
=> x = 10,000

That stone of 2 kg breaks into two on falling in the ratio 3 : 2

Therefore wights of those pieces separately now = 1.2 kg and 0.8 kg

So, price of the bigger piece = 1.2²x = 1.44 × 10,000 = 14,400
And the price of the smaller one = 0.8²x = 0.64 × 10,000 = 6,400

Therefore the loss = 40,000 – (14,400 + 6,400) = 19,200 (option ‘C’)

QUERY 42

By selling an article for Rs 720, a man losses 10%. At what price should he sell it to gain 5%?

A) Rs 840
B) Rs 800
C) Rs 750
D) Rs 820

MAHA GUPTA
Cost price of the article = 720(100/90) = 800

Now the new selling price = C. P. + 5% of C.P. = 800 + 5% of 800 = 840 (option ‘A’)

QUERY 43

If selling price of an article doubles, the profit triples. Find profit percentage?

A) 100%
B) 50%
C) 75%
D) 150%

MAHA GUPTA
Let the initial selling price = Rs 100; of course it has one part of cost price and one part of profit

After it got doubled the selling price = Rs 200
Obviously the its additional amount Rs 100 has profit only (no part of cost). As the profit triples it’s easy to understand that this has 2 parts of profit of Rs 50 each.

Means the initial sales price too has Rs 50 as profit
Therefore cost price of the article = Sales Price – Profit i.e. 100 – 50 = Rs 50

Means Rs 50 as profit on cost of Rs 50, means percentage of profit = 100% (option ‘A’)

QUERY 44

The cost of a piece of diamond varies with the square of its weight. A diamond of Rs 5184 value is cut into 3 pieces whose weight are in the ratio 1 : 2 : 3. Find the loss involved in the cutting.

A) Rs 3068
B) Rs 3088
C) Rs 3175
D) Rs 3168

MAHA GUPTA
As the price varies with square of weight, there must be a constant part of price.

Now let that constant part of price = Rs x, and weight of the piece of diamond be 6 kg
So we can say 6²x = 5,184
=> x = 144

That stone of 6 kg is cut into the ratio 1 : 2 : 3

Therefore wights of those pieces separately now = 1 kg, 2kg and 3 kg

So, price of the smallest piece = 1²x = 1 × 144 = 144
Price of the medium piece = 2²x = 4 × 144 = 576
And price of the biggest piece = 3²x = 9 × 144 = 1296

Therefore the loss = 5,184 – (144 + 576 + 1296) = 3168 (option ‘D’)

QUERY 45

A radio was sold at 16% profit. If it was bought for less by 10% and was sold for less by Rs 14, it would have been the profit of 25%. Find the cost price of the radio.

A) Rs 200
B) Rs 500
C) Rs 400
Rs Rs 350

MAHA GUPTA
Let the cost price of the radio = 100
Therefore the selling price = 100 + 16% of 100 = 116

The new cost price = 100 – 10% of 100 = 90
But it would have been the profit of 25% then, therefore the new selling price = 90*(125/100) = 112.50

The difference of two selling price = 116 – 112.50 = 3.50

Now, if the difference of the selling prices is 3.50, the cost price = 100
If the difference is 14, the cost price = (100/3.50)*14 = 400 (option ‘C’)

QUERY 46

A man gives 4 percent discount on the marked price and gives 1 article free for buying every 15 articles and thus gains 35 percent. The market price is increased above the cost price by?

A) 35%
B) 40%
C) 42%
D) 50%

MAHA GUPTA
Let the marked price = 100
This price after discount of 4% = 100 – 4 = 96

But again he gives 1 article free on buying of 15 articles; means discount of 1 on every set of 16. Therefore discount on 96 = 96/16 = 6

Therefore total discount = 4 + 6 = 10%
Hence the selling price = 100 – 10 = 90

Now his gain is 35%
So if the selling price is 135 the cost price = 100
If the selling price is 90 the cost price = (100/135)*90 = 200/3

Hence excess of marked price over cost price = 100 – 200/3 = 100/3

Now we must find it in percentage as the marked price is an assumed one

Increase on 200/3 = 100/3
Hence increase on 100 = (100/3)(3/200)100 = 50% (option ‘D’)

QUERY 47

A house and a shop were sold for 1 lac each, house loses by 20% and shops gained by 20%, what is over all result of all business?

A) 1/24 lac loss
B) 1/12 lac loss
C) 1/18 lac loss
D) Profit

MAHA GUPTA
Total Selling Price = 1,00,000 + 1,00,000 = 2,00,000

Cost Price of the house = (100/80)*1,00,000 = 1,25,000
Cost Price of the shop = (100/120)*1,00,000 = 2,50,000/3
Therefore total Cost Price = 1,25,000 + 2,50,000/3 = 6,25,000/3

We see the cost price is more than the selling price, so it’s a loss.

Hence the loss = 6,25,000/3 – 2,00,000 = 25,000/3 thousand = 25,000/3,00,000 lac = 1/12 lac (option ‘B’)

QUERY 48

By selling an article for 2850, a person gain 14%. If the profit reduced to 8% then selling price will be?

A) Rs 2550
B) Rs 2600
C) Rs 2700
D) Rs 2750

MAHA GUPTA
The new selling price (SP) = Old SP*(100+new rate of profit/100+old rate of profit)
= 2850*(108/114) = 2700 (option ‘C’)

QUERY 49

A pen is listed for Rs 12. A discount of 15% is given on it. A second discount is given bringing the prize down to Rs 8.16. The rate of the second discount is?

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

MAHA GUPTA
Discount at 15% on 12 = 1.80
Therefore the price after = 12 – 1.80 = 10.20

Thus the second discount = 10.20 – 8.16 = 2.04

But this discount is on 10.20
Hence the second discount in percentage = (2.04/10.20)*100 = 20 (option ‘A’)

ANOTHER APPROACH
Overall discount = 12 – 8.16 = 3.84
In percentage = (3.84/12)*100 = 32%

The formula for finding overall discounts when two successive discounts are there
a + b + ab/100, where a and b are the discounts

Now therefore, a + b + ab/100 = 32
=> 15 + b + 15b/100 = 32
=> b = 20% (option ‘A’)

QUERY 50

On selling an item the profit is 20%. By giving 30% discount on the item, the sale of that item increases by 60%, so what is his gain or loss % now?

A) 16% gain
B) 16% loss
C) 20% gain
D) 20% loss

MAHA GUPTA
Let the cost price of the item = 100
Hence the selling price = 100 + 20% of 100 = 120

But now he is giving a discount of 30%, hence the effective selling price = 120 – 30% of 120 = 84

Hence it will be a loss of 100 – 84 = 16% (option ‘B’)