Naman bought a few apples for Rs 720 from a shop. He negotiated the price and the shopkeeper reduced it by Rs 2 per apple. Due to this Naman could buy four more apples than what he had bought earlier. How many apples did he originally buy?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 36.
Let the rate of the apples be x and the quantity be y.
x × y = 720 ----- (1)
As he bargains, the price reduces by 2, and the quantity increases by 4
⇒ (x - 2) × (y + 4) = 720 ---- (2)
Fom eq 1 and 2
⇒ (x - 2) × (y + 4) = xy
⇒ xy - 2y + 4x - 8 = xy
⇒ 2x - y = 4 ---- (3)
⇒ x = (4 + y)/2 ---- (4)
Using equation (4) in equation (1), we get
⇒ [(4 + y)/2] × y = 720
⇒ y2 + 4y = 1440
Solving the quadratic equation;
⇒ y = 36
Hence, Naman originally bought 36 apples.