Problem: Find the rate of interest per annum, at which the simple interest on a certain sum becomes 2/5 times of amount in 10 years at simple interest.

Solution:

Let us assume that the principal amount is P.

We know that,

Simple Interest = (P x R x T)/100

where,
R = Rate of Interest per annum
T = Time in years

Amount = Principal + Simple Interest

Given, Simple Interest = 2/5 of Amount

So, (2/5) x Amount = Principal + Simple Interest

=> (2/5) x (Principal + Simple Interest) = Principal + Simple Interest

=> 2 x Principal = 3 x Simple Interest

=> Simple Interest = (2/3) x Principal

We also know that,

Amount = Principal + Simple Interest

=> Amount = Principal + (2/3) x Principal

=> Amount = (5/3) x Principal

We need to find the rate of interest per annum at which the simple interest on a certain sum becomes 2/5 times of amount in 10 years at simple interest.

Let us assume that the rate of interest per annum is R%.

So, Simple Interest = (P x R x T)/100 = (P x R x 10)/100 = (P x R)/10

Substituting the values of Simple Interest and Amount, we get:

(2/3) x Principal = (P x R)/10

=> R = (20/3)%

Therefore, the rate of interest per annum at which the simple interest on a certain sum becomes 2/5 times of amount in 10 years at simple interest is 6.67%.

Answer: The rate of interest per annum at which the simple interest on a certain sum becomes 2/5 times of amount in 10 years at simple interest is 6.67%.