Question

In how many years the interest on Rs 1200 at 5% simple interest per annum is equal to the interest on Rs 800 at 7.5% simple interest per annum in 2.5 years?

Answer 1

Answer:

In 0.25 years the first interest and second interest will be equal.

Step-by-step-explanation:

For first simple interest,

• Principal ( P₁ ) = Rs 12000
• Time ( N₁ ) = x years
• Rate of interest ( R₁ ) = 5 %

For second simple interest,

• Principal ( P₂ ) = Rs 800
• Time ( N₂ ) = 2.5 years
• Rate of interest ( R₂ ) = 7.5 %

We have to find the number of years in which first interest will be equal to second interest.

∴ First simple interest = Second simple interest

We know that,

Simple interest = ( Principal * Rate * Time ) / 100

⇒ ( P₁ * N₁ * R₁ ) / 100 = ( P₂ * N₂ * R₂ ) / 100

⇒ P₁ * N₁ * R₁ = P₂ * N₂ * R₂

⇒ 12000 * x * 5 = 800 * 2.5 * 7.5

⇒ 12000 * 5 * x = 800 * 5 / 2 * 15 / 2

⇒ 60000x = 4000 / 2 * 15 / 2

⇒ 60000x = 4000 / 4 * 15

⇒ 60000x = 1000 * 15

⇒ x = 1000 * 15 / 60000

⇒ x = 1000 / 4000

⇒ x = 1 / 4

⇒ x = 0.25

Time = 0.25 years

∴ In 0.25 years the first interest and second interest will be equal.