​The ratio of simple interest earned on a certain amount at the rate of 5% and 8% for 6 years and 3 years respectively is:​

Correct option is A

Given:

​Case 1: Rate of interest = 5%, Time = 6 years

Case 2: Rate of interest = 8%, Time = 3 years

Formula Used:

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

Where:

$P$ = Principal amount

$R$ = Rate of interest (per annum)

$T$ = Time (in years)

Solution:

For,  Rate of interest = 5%, Time = 6 years

SI₁=  $$\frac{P\times 5\times 6}{100}$$=$$\frac{30P}{100}$$ = 0.3P

For, Rate of interest = 8%, Time = 3 years

SI₂=   $$\frac{P\times 8\times 3}{100}$$ =  $$\frac{24P}{100}$$ = 0.24P

Ratio of Simple Interest,

Ratio = $$\frac{0.3P}{0.24P}$$= $$\frac{30}{24}$$ = $$\frac{5}{4}$$ 

The ratio of the simple interest earned is 5 : 4.​

Thus, Option (A) is right.