The simple interest of a principal in `1` year and `9` months at the rate of simple interest of `5%` per annum is `63Rs` more than of the same principal in `2` years and `4` months at the rate of simple interest of `4(1)/(2)%` per annum. Find the principal.

Explanation

`1` year and `9` months `=(1+(9)/(12))` years `=(7)/(4)` years.
Similarly, `2` years and `4` months `=(2+(4)/(12))` years `=(7)/(3)` years.
Now, let the principal be `Rs x`.
So, the simple interest of `Rs x` in `(7)/(4)` years at the rate of `9%` simple interest per annum
`=Rs(x xx5xx7)/(100xx4)=Rs(7x)/(80)`
Again, the simple interest of `Rs x` in `(7)/(3)` years at the rate of `4(1)/(2)%` simple interest per annum
`=Rs(x xx9xx7)/(100xx2xx3)=Rs(21x)/(200)`
As per question, `(21x)/(200)-(7x)/(80)=63implies(42x-35x)/(400)=63`
or, `(7x)/(400)=63` or, `7x=63xx400` or, `x=(63xx400)/(7)` or, `x=3600`
`:.` The required prinicpal `=Rs3600`