Question

Mukund has ₹ 50 more than Sagar. If the product of the amount they have is 15,000, then find the amount each has.

Answer 1

Let Sagar possesses ₹ x.

∴ The amount Mukund possesses = ₹ (x + 50)

According to the given condition, the product of the amount they have is ₹ 15,000.

∴ x(x + 50) = 15000

∴ x² + 50x – 15000 = 0

∴ x² + 150x – 100x – 15000 = 0   ...`[(-15000 = 150; -100),(150 xx (-100) = -15000),(150 - 100 = 50)]`

∴ x(x + 150) – 100(x + 150) = 0

∴ (x + 150)(x – 100) = 0

By using the property, if the product of two numbers is zero, then at least one of them is zero, we get

x + 150 = 0 or x – 100 = 0

∴ x = –150 or x = 100

But, amount cannot be negative.

∴ x = 100 and x + 50 = 100 + 50 = 150

∴ The amount possessed by Sagar and Mukund are ₹ 100 and ₹ 150 respectively.