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Rajesh Prasad Lala
Asked: 2022-11-08T14:39:51+05:30 In:

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.

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.
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  1. `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`

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