Naman bought a certain number of apples for ₹720. After negotiating, the shopkeeper reduced the price by ₹2 per apple, allowing Naman to buy four more apples for the same amount. Find the number of apples Naman originally bought.

Question

Accepted Answer

Let the original number of apples bought be x, and the original price per apple be p.

So, x × p = 720  ...(1)

After the price is reduced by ₹2 per apple, Naman can buy 4 more apples for the same amount:

New price per apple = p - 2
Number of apples bought now = x + 4
So, (x + 4) × (p - 2) = 720  ...(2)

Now, expand equation (2):
(x + 4)(p - 2) = 720
xp - 2x + 4p - 8 = 720
But xp = 720 (from equation 1), so substitute:
720 - 2x + 4p - 8 = 720
-2x + 4p - 8 = 0
4p - 2x = 8
2p - x = 2
x = 2p - 2

Now substitute x in equation (1):
(2p - 2) × p = 720
2p^2 - 2p = 720
2p^2 - 2p - 720 = 0
Divide both sides by 2:
p^2 - p - 360 = 0

Solve the quadratic equation:
p^2 - p - 360 = 0

Factorizing:
(p - 19)(p + 18) = 0
So, p = 19 (since price cannot be negative)

Now, x = 2p - 2 = 2×19 - 2 = 38 - 2 = 36

Therefore, Naman originally bought 36 apples.

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