If the interest of a principal in `10` years be `(2)/(5)th` part of itself, then find the yearly percentage of rate of simple interest.

Explanation

Let the principal be `Rs x` and the yearly rate of simple interest be `r %`
`:.` The interest of `10` years `=Rs(x xxrxx10)/(100)=Rs(xr)/(10)`
`:.` Amount `=Rs(x+(xr)/(10))`
As per question, `(2)/(5)(x+(xr)/(10))=(xr)/(10)`
`implies(2x)/(5)+(2)/(5)xx(xr)/(10)=(xr)/(10)=(xr)/(10)implies(2x)/(5)=(xr)/(10)-(xr)/(25)`
`implies(2x)/(5)=(5xr-2xr)/(50)`
`implies(2x)/(5)=(3xr)/(50)`
`impliesr=(2x xx50)/(5xx3x)=(20)/(3)=6(2)/(3)`
`:.` Anuual rate of interest `=6(2)/(3)%`