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?

Solution

Let the original price per apple be x and the number of apples bought initially be n.

Step 1: Initially, the number of apples is:
n = 720 / x

Step 2: After the price reduction, the new price is (x - 2), and the number of apples becomes:
n + 4 = 720 / (x - 2)

Step 3: Substitute n = 720 / x into the second equation:
(720 / x) + 4 = 720 / (x - 2)

Step 4: Simplify the equation:
720 / (x - 2) - 720 / x = 4
(720 * 2) / [x(x - 2)] = 4
1440 / [x(x - 2)] = 4

Step 5: Multiply through by x(x - 2):
1440 = 4x(x - 2)

Step 6: Simplify the quadratic equation:
1440 = 4x² - 8x
x² - 2x - 360 = 0

Step 7: Solve for x by factorization:
(x - 20)(x + 18) = 0
x = 20 (as price must be positive).

Step 8: Calculate n:
n = 720 / x = 720 / 20 = 36

Answer

Naman originally bought 36 apples.