Question

If a simple interest on a sum of money at 6% p.a. for 7 years is equal
to twice of simple interest on another sum for 9 years at 5% p.a.. The
ratio will be :
(a) 2:15
(b) 7:15
(c) 15:7
(d) 1:7
​

Answer 1

Given: Simple interest on a sum of money (Principal) at 6% p.a. for 7 years is equal to twice of simple interest on another sum (Principal) for 9 years at 5% p.a.

To find: The ratio of Principal amounts

Let: The principal amounts be $P_{1} \ and \ P_{2}$

Solution: Given that,

On $P_{1}$

Simple rate of interest (R) = 6% p.a.

Time (T) = 7 years

On $P_{2}$

Simple rate of interest (R) = 5% p.a.

Time (T) = 9 years

∵ $Simple \ Interest = \frac{P \ * \ R \ * \ T}{100}$

Now, according to the question,

∵ $\frac{P_{1} \ * \ 6 \ * \ 7}{100} = 2 (\frac{P_{2} \ * \ 5 \ * \ 9 }{100} )$

⇒ $\frac{P_{1} \ * \ 42 }{100} = 2(\frac{P_{2} \ * \ 45}{100})$

⇒ $P_{1} \ * \ 21 = P_{2} \ * \ 45$

⇒ $\frac{P_{1} }{P_{2} } = \frac{45}{21} \ or \ \frac{15}{7}$

Hence, the ratio will be 15 : 7.

Answer 2

step by step explanation

answer option c