Question

A sum of money becomes 140% of itself in 5 years. In how many years it will double itself at the same rate of simple interest?
1. 10
2. \(\dfrac{25}{2}\)
3. 15
4. \(\dfrac{21}{2}\)

Answer 1

Correct Answer - Option 2 : \(\dfrac{25}{2}\)

Given:

A sum of money becomes 140% of itself in 5 years

Formula used:

Simple Interest = (Principal × Rate × Time)/100

Amount = Principal + Simple Interest

Calculation:

According to the question:

Amount = 140% × Principal

⇒ Amount/Principal = 140/100 = 7/5

Let the amount be Rs. 7x

And principal be Rs. 5x

Amount = Principal + Simple Interest

⇒ 7x - 5x = Simple Interest

⇒ Simple Interest = 2x

Now,

Simple Interest = (Principal × Rate × Time)/100

⇒ Simple Interest = (5x × R × 5)/100

⇒ 2x = Rx/4

⇒ R = 8%

Again,

According to the question:

Amount = 2Principal

Principal + Simple Interest = 2Principal

Simple Interest = 2Principal - Principal = Principal

⇒ Simple Interest = Principal 

Now,

Simple Interest = (Principal × Rate × Time)/100

⇒ Principal = (Principal × 8 × Time)/100

⇒ Time = 100/8 = 25/2 years

∴  25/2 years it will double itself at the same rate of simple interest.