A trader offers to sell a commodity under any of the two schemes mentioned below:
Scheme 1: The trader offers two successive discounts of 20% and 12.5% on the sale of each unit.
Scheme 2: The trader offers the buyer an option to 'pay for y units, get z units free'. The buyer realizes that if he needs to buy (y + z) units, it does not matter to him which of the two schemes he opts for.
Which of the following options gives a correct ordered pair of (y, z)?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. (7, 3).
Scheme 1:
Let the price = 100
Final price = 100 × (80/100) × (87.5/100) = 70
Net discount = 30%
Scheme 2:
For (y + z) units, effective price = y units (pay for y, get z free)
z/(y + z) = 30/100
⇒ z = 0.3y + 0.3z
⇒ y/z = 7/3
Hence, the correct ordered pair of (y, z) is (7, 3).