Profit and Loss | Set2 (original) (raw)

Last Updated : 24 Dec, 2025

Profit and Loss is an important topic in arithmetic that deals with the buying and selling of goods. When an article is sold at a price higher than its cost price, the seller makes a profit. When it is sold at a price lower than its cost price, the seller incurs a loss. This concept is widely used in daily life, business, and trade to calculate gain, loss, and percentage profit or loss.

We will solve these questions using the Profit and loss formula :

Questions Set for Profit & Loss

**Question 1: The cost price of 12 books is equal to the selling price of 10 books. The gain percent is:

**Solution :

Given 12 CP = 10 SP CP/SP = 10/12 = 5/6 Profit = SP - CP
=> 6 - 5 = 1 Profit (%) = profit/CP x 100
=> 1/5 x 100
=> 20 %

**Question 2: If the loss% on the article is 15%. Then the ratio of the cost price and the selling price will be

**Solution :

Loss % = 15 % = 15/100 = 3/20
Loss= 3 and CP = 20
SP = CP - L = 20 - 3 = 17
CP : SP = 20 : 17

**Question 3: Ram goes from place P to Q to buy an article costing 20% less at Q. Although he spends Rs 200 on travelling, still he gains Rs 200 compared to buying at P. His profit percent is:

**Solution :

Let the price at P = 100a then price at Q = 80a (20% less)

Acc. to question

100a - (80a + 200) = 200
20a = 400 a = 20
Price at P = 100x20 = 2000

Price at Q including travelling = 80x20 + 200 = 1800
Profit (%) = [(2000 - 1800) / 2000]x100 =200/20 = 10%
Hence, his profit is **10%.

**Question 4: The price of a TV and a refrigerator set are in ratio 3:5. If the refrigerator cost Rs 4400 more than the TV set, then the price of the TV is

**Solution :

Acc. to question TV/Ref. = 3/5 Difference in ratio = 2 2 -> 4400 1 -> 2200 The price of the TV = 3x2200 = Rs 6600

**Question 5: A house and a shop were sold for Rs. 1 lakh each. In this transaction, the house sale resulted into 20% loss whereas the shop sale into 20% profit. The entire transaction resulted in:

**Solution : Acc. to question

House Shop
CP 10 10
|-20% |+20%
SP 8 12

Make SP equal

CP 10x12 10x8 -> 200
|-20% |+20% |-8
SP 8x12 12x8 -> 192

Given that 192 -> 2 lakh 1 -> 1/96 8 unit -> 8/96 -> 1/12 lakh Hence, in entire transaction loss is **1/12 lakh

**Question 6: A shopkeeper sells a chair at a profit of 20%. If he had bought the table at 10% less cost and sold for Rs 60 more, he would have gained 40%. The cost price of the chair is:

**Solution :

Let 100 units is the CP of chair. Sells at profit 20% than SP = 120 If buys 10% less and sells at 40% profit than SP = 126
-10%
(CP)100 ______________(New CP)90
|+20% |+40%
(SP)120 (New SP)126

So, difference in SP and New SP is given 60 126 - 120 = 6 6 -> 60 1 -> 10 100 -> 1000 Hence, the cost price of chair is **Rs 1000

****Question 7:**By selling a bicycle of Rs 3360 a shopkeeper gain 12%. If the profit is reduced to 8%, then the selling price will be

**Solution :

SP of bicycle = Rs 3360 Profit % = 12 % CP = (SP/100+P)x100 CP = (3360/112) x 100 New profit% = 8% New SP = CPx(100+P%)/100 = (3360/112)x100x(108/100) = 3240 Hence, the selling price of bicycle is Rs 3240 .

**Question 8: A man purchased an article of Rs 2500 and sold it at 40% above the cost price. If he has to pay Rs 250 as tax on it his net profit percentage will be:

**Solution :

CP = 2500 P =40% Profit = CPx25/100 = 2500x40/100 = 1000 Net profit = profit - tax = 1000 - 250 = 750 Net profit % = 750/2500 x 100 =30% Hence, net profit percent is **30%.

**Question 9: A sells an item to B at a profit of 25%. B sells it to C at a profit of 20%. If C pays Rs 900 for it, the cost price of the bicycle for A is :

**Solution :

A B C
100___25% profit____ 125____20% profit___150

Now, 150 unit -> 900 1 unit -> 6 100 unit -> 600 Hence, the cost price of the bicycle is **600.

**Question 10: A increase of 20% in the price of apple enabled a purchaser to obtain 4 apple less of Rs 72. The price of 16 apple before increase was

**Solution :

Price 5 20% increase 6
Commodity 6 1 unit less 5
|x4 | |x4
24 apples 4 apples 20 apples

He purchased 24 apples of Rs 72 before increase of price and 4 less apples after increase. 24 apples = Rs 72 1 apple = Rs 3 16 apples = Rs 48

**Question 11: Shyam buys some chocolates at 2 for a rupee and sells them at 5 for a rupee. His loss percent is:

**Solution :

Acc. to question

Chocolates Price
CP 2x5=10 1x5=5
loss 3
SP 5x2=10 1x2=2

make chocolates same and we loss Rs 3 here. So, Loss% = 3/5 x 100 = 60%

**Question 12: By selling 100 oranges, a shopkeeper gains the selling price of 20 oranges. His gain percent is:

**Solution :

Let SP of 1 orange is Rs 1.
SP of 100 orange is Rs 100.
CP of 1 orange is Rs a.
CP of 100 orange is Rs 100a.

Acc . to question

Gain=SP - CP 20 = 100 - 100a

a = 80/100 = 4/5

CP of 1 orange = 4/5 CP of 100 orange = 100x4/5= 80
SP of 100 orange = Rs 100
gain% = 20/80 x 100 = 25%

Hence, his gain percent is 25%.

**Question 13: A dealer gives a 10% discount on the advertised (marked) price of a scooter. Even after giving this discount, he makes a profit of 20% on the cost price. If the profit earned is ₹7,200, find the advertised price of the scooter.

**Solution :

Profit = 20% of CP
So,
20% of CP = 7,200

CP = 7,200 × 10020 = ₹36,000

Selling Price (SP) = CP + Profit

SP=36,000+7,200=₹43,200

Given 10% discount,

SP=90% of MP

MP=43,200×10090=₹48,000

**Question 14: A shopkeeper allows a discount of 22% on the marked price. How much above the cost price must he mark his goods as to gain 17%?

**Solution :

Acc. to question

CP MP
100 - discount : 100 + profit
100 - 22 : 100 + 17
78 : 117
2 : 3

3 - 2 = 1

Raised% = 1/2 x 100 = 50%

Hence, he has to mark his goods 50% above of CP.