# QUESTIONS ON PROFIT & LOSS (PART-V)

## 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’)