The simple interest for a certain sum of money is half the principal. Find the time and rate of interest if the rate is twice the time.

A 5 years, 10%

B 10 years, 5%

C 4 years, 8%

D 4.5 years, 9%

E None of these

Correct Answer: Option A

Let the Principal be ‘a’.

∴ Interest = a/2

Let the time be ‘t’ years. Since the rate is twice the time,

∴ Rate of interest = 2 × t = 2t%

We know that,

Simple Interest = (P × R × T)/100

Where, P = principal Amount, R = % Rate of interest, T = time period in years

Here, P = a; R = 2t; T = t; SI = a/2

\(\therefore \frac{a}{2}\; = \;\frac{{a\; \times \;t\; \times \;2t}}{{100}}\)

⇒ 2t2 = 50

⇒ t2 = 25

⇒ t = 5

∴ Time = t = 5 years

⇒ Rate of interest = 2t = 2 × 5 = 10 %