If the selling price of an article is 3 times the discount offered and if the percentage of the discount is equal to the percentage profit, find the ratio of the discount offered to the cost price.

Correct option is B

Given:

S.P = 3 (Discount)

D% = P%

Formula used:

Discount = MP − SP

D% = [(MP - SP)/MP] × 100

P% = [(SP - CP)/CP] × 100

Solution:

SP = 3 × discount

=> S.P = 3(MP − SP)

=> S.P = 3M.P − 3S.P

=> 4S.P = 3 M.P

=> $$\frac{S.P}{M.P} = \frac{3}{4}$$​​

Now we are given that:

D% = P%

=> [(MP - SP)/MP] × 100 = [(SP - CP)/CP] × 100

=>  $$\frac{(4-3)}{4}$$  = [(SP - CP)/CP] 

=> $$\frac{1}{4}$$= [(SP - CP)/CP]

=> 1/4 = (SP/CP) - 1

=> SP/CP = 1/4 + 1 = 5/4

=>  $$\frac{S.P}{C.P} = \frac{5}{4}$$​​

Now Ratio of CP, SP and MP is:

CP : SP : MP

4    :  5

         3 :   4 

12 : 15 :  20 

Therefore,  

$$\frac{Discount}{CP} = \frac{MP - SP}{CP} = \frac{20-15}{12} = \frac{5}{12}$$

Hence, option (b) is the correct answer.

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