If the selling price of a book is 8 times the discount offered and if the percentage of...
Qualcomm technical mcq question, verified with a worked answer. Free to practise - no sign-up.
If the selling price of a book is 8 times the discount offered and if the percentage of discount is double the percentage of profit, then what will be the ratio of the discount offered to the cost price?
Show answer & explanation
Let D = discount, CP = cost price, SP = selling price, and profit% = P. From the given conditions: SP = 8D and discount% = 2P. Using the relationships SP = CP(1 + P/100), D = MRP - SP, and discount% = D/MRP × 100, we can derive that D/CP = 19/144 through algebraic manipulation of these constraints.
Step-by-step Derivation:
Let D = discount offered, CP = cost price, SP = selling price, MRP = marked price.
Given:
- SP = 8D
- Discount% = 2 × Profit%
Let profit% = P, then discount% = 2P
We know:
- Profit% = (SP - CP)/CP × 100 = P
- Discount% = (MRP - SP)/MRP × 100 = 2P
- Discount D = MRP - SP
From profit%: SP = CP(1 + P/100)
From discount%: D/MRP = 2P/100
→ D = MRP × 2P/100
Also: MRP - SP = D
→ MRP = SP + D = 8D + D = 9D
Substituting into discount% formula:
2P/100 = D/(9D) = 1/9
→ P = 50/9
From SP = 8D and SP = CP(1 + P/100):
8D = CP(1 + 50/900)
8D = CP(1 + 1/18)
8D = CP(19/18)
Therefore:
D/CP = 19/(8 × 18) = 19/144
Ratio of discount to cost price = 19:144