Question

A shopkeeper gives a 5% discount on the marked price of an article and still makes a profit of 14%. If he gains Rs. 84 on the article, then which of the following is correct?

A. Cost price of the article is Rs. 540

B. Selling price of the article is Rs. 684

C. marked price is 20% more than the cost price.

D. Cost price is a multiple of 100.

1. Only A
2. A and B
3. B, C, and D
4. C and D

Answer 1

Correct Answer - Option 3 : B, C, and D

Given:    

Discount% = 5%

Profit% = 14%

Profit = Rs. 84                          

Formula Used:

Profit% = (Profit/CP) × 100

Discount% = (Discount/MP) × 100

SP = {(100 + P%)/100} × CP

SP = {(100 – D%)/100} × MP

Where P is Profit, D is discount, CP is cost price, SP is selling price and MP is maximum retail price.

Calculation:

Profit = 14% of CP

⇒ 84 = (14/100) × CP

⇒ 84 × 14/100 = CP

⇒ CP = Rs. 600

A. Cost price of the article is Rs. 540

CP = 600

⇒ A is incorrect

B. Selling price of the article is Rs. 684

SP = {(100 + 14)/100} × 600

⇒ SP = 114 × 6

⇒ 684

⇒ B is correct

C. marked price is 20% more than the cost price.

Discount% = 5%

SP = {(100 – 5/100} × MP

⇒ 684 = (95/100) × MP

⇒ MP = 720

MP – CP = 720 – 600

⇒ 120

% difference = ((MP – CP)/CP) × 100%

⇒ (120/600) × 100%

⇒ 20%

⇒ C is correct

D. Cost price is a multiple of 100.

⇒ CP = 600

⇒ 6 × 100

⇒ D is correct

∴ B, C, and D are correct