Question

A sum of money lent at simple interest amounts to $Rs.783$ in $2$ years and to $Rs.837$ in 3 years. Find the sum and the rate per cent per annum.

Answer 1

Amount in $3$ years (Principal $+$ S.I. for $3$ years) = $Rs.837$ ...(i)

Amount in $2$ years (Principal $+$ S.I. for $2$ years) = $Rs.783$ ...(ii)

On subtracting (ii) from (i),

Interest earned in $1$ year = $(837-783)=Rs.54$

$\therefore$ Interest earned in $2$ years = $54\times \times 2=Rs.108$

$\therefore$ Sum = Amount for $2$ years $-$ S.I. for $2$ years = $783-108$

= $Rs.675$

Now, $P=Rs.675,S.I.=Rs.108$ and $T=2$ years

$\therefore R=\frac{S.I.\times 100}{P\times T}$

$=\frac{108\times 100}{675\times 2}=8\%$

Hence, sum is $Rs.675$ and the rate per cent per annum is $8\%$.