Numerical Ability Profit and Loss Sample Questions with Explanation

PROFIT & LOSS

★ Cost Price (C.P.): The Price at which the article is bought.

★ Selling Price (S.P.): The price at which the article is sold.

★ Profit = Selling Price − Cost Price

★ Loss = Cost Price − Selling Price Profit

★ Profit % =Profit/Cost Price × 100

 

★ Loss % = Loss/Cost Price × 100

Ex: A student buys a book for Rs.1,250 and sells for Rs.1,437.50. Find his profit percent?

Sol: Profit % = ((1437.50 – 1250)/1250) × 100

⇒ (187.50/1250)× 100 = 15%

Note: Profit or loss percent is always calculated on Cost Price unless it is asked to be calculated on Selling Price.

★ Cost Price

⇒ ( 100/100+Profit %) × Selling Price  [OR] (100/100 − Loss %) × Selling Price

★ Selling Price

⇒(100 + Profit %/100) × Cost Price  [OR]  (100 − Loss %/100) × Cost Price

Ex: The owner of an electronic store charges his customer 11% more than the cost price. If a customer paid Rs.1,33,200 for an LED TV, what was the original price of the TV? (RBI Assts 2012)

A) Rs.1,20,000 B) Rs.1,14,500

C) Rs.1,22,500 D) Rs.1,18,000

E) None of these

Sol: S.P. = Rs.1,33,200, P% = 11%

 C.P. =100/(100 + 11%) × 133200

⇒ (100/111) × 133200 = Rs.120000

Shortcut: Cost price is 100%, Profit = 11% therefore S.P. = 111%

If  116% value is 1,33,200 then

 100% = (100/111)× 133200

= Rs.1,20,000

Discounts:

★ The price at which the article is marked above cost price is called the marked price or labelled price or listed price or catalogue price or printed price etc.

★ The discount is allowed on marked price.

★ Discount% = (Discount/ Marked Price)  × 100

Note: Discount percents are always calculated on Marked Price.

★ When discount is deducted from the marked price, the remainder becomes the selling price.

Ex:A dealer marked on article atRs. 2,140 and sells for Rs.1,712. Find the discount percent he has offered?

A) 21% B) 25% C) 20%

D) 16% E) None of these

Sol: Discount% =((2140 – 1712)/2140) × 100

⇒  (428 /2140)× 100 = 20%

★ To find Marked Price from Cost Price, the following formula can be used.

★ Marked Price

= ((100 + Profit%)/(100-Discount%)) × Cost Price

Ex:A trader buys an article for Rs.5,160. He allows 14% discount on it. If he gains 12% on the article, find  the rate at which he marked the article?

A) Rs.5,675 B) Rs.6,380

C) Rs.6,720 D) Rs.6,525

E) None of these

Sol: C.P. = 5160, Profit% = 12%, Discount% = 14%

 M.P. =((100 + 12) /(100-14)) × 5160

⇒(112/86) × 5160

= Rs.6,720

Some More Models

1. The cost of 12 chairs and 15 tables is Rs.58,968. What is the cost of 4 chairs and 5 tables?

A) Rs.19,656 B) Rs.29,484 C) Rs.39,312 D) Can't be determined E) None of these

Sol: Given, 12 chairs and 15 tables cost price as Rs.58,968. 4 chairs & 5 tables are one-third of given numbers.

∴ Cost price of 4 chairs & 5 tables

= 58968/3

= Rs.19,656

2. A shopkeeper sold an article for Rs.425, there by losing 15%. At what price should he have sold the article to earn a profit of 10%?

A) Rs.580 B) Rs.550 C) Rs.520 D) Can't be determined E) None of these

Sol: S.P. = Rs.425, Loss % = 15%

∴ C.P. =100/85 × 425 = Rs.500

Now CP of the article is Rs.500

Profit = 10%

∴ S.P. =(110/100) × 500 = Rs.550.

Shortcut: If 85% value (1st S.P.) is Rs.425, then 110% value (2^nd S.P.) is

=(110/85) × 425 = Rs.550

3. A man buys a scooter at Rs.6,250 and spent Rs.1,250 on its repairs. He had to sell it for Rs.6,750. Find his profit or loss percent?

A) 10% Profit B) 25% Loss C) 10% Loss D) 15% Profit E) None of these

Sol: C.P. = Rs.6,250 + Rs.1,250 = Rs.7,500

S.P. = Rs.6,750

∴ Loss = Rs.7500 − Rs.6750 = Rs.750

Loss% =(750/7500) × 100 = 10%

4. A sells an article to B at a gain of 10% and B sells it to C at a gain of 5%. If C pays Rs.4,620 for it, what did it cost to A?

A) Rs.4,550 B) Rs.3,250 C) Rs.5,250 D) Rs.4,000 E) None of these

Sol: Let the cost price of A be Rs.100, then the selling price =Rs.110.  Now, the cost price of B be Rs.110

 Selling price of B =105/100 × 110 100 231 = Rs. 132/2

∴ C.P. of C = 231/2

But the cost price of C as given = Rs.4,620

If the cost price of C is Rs. 231/2,

then the C.P. of A = Rs.100

If the cost price of C is Rs.4,620 then the

C.P of A=(100 × 2 × 4620)/ 231

= Rs.4,000

Shortcut:

Let the C.P. of A be Rs. x then

110% of 105% of x = Rs.4,620

⇒  (110 /100)×(105/100) × X = 4620

⇒ x = 4620 ×100/110 ×100/105

= Rs.4,000

5. A dishonest dealer professes to sell his goods at the cost price, but uses only 960 grams in place of a kilogram weight. Find his profit percent?

A) 20% B) 25% C) 30% D) 15% E) None of these

Sol: Profit % =(Original Weight − False Weight)/False Weight × 100

⇒ P % = (1000-960)/960× 100

⇒40/960 × 100 = 4 1/6 %