Question

The simple interest on a certain sum for 3 and half years at 7% p.a. is Rs.225 more than the simple interest on the same sum for 4 years at 5% p.a. Find the sum.

Answer 1

Let the sum be x

case (i) 
Principle = x, Rate = 7%, time = 3.5 yrs
Interest = $\frac{PTR}{100}$
= $\frac{x (7)(3.5)}{100}$
= $\frac{24.5x}{100}$

case (ii) 
Principle = x, Rate = 5%, time = 4 yrs
Interest = $\frac{PTR}{100}$
= $\frac{x (5)(4)}{100}$
= $\frac{20x}{100}$

given that, the simple interest for case (i) is Rs 225 more than the simple interest for case (ii)

$\frac{24.5x}{100} - \frac{20x}{100} = 225$

$\frac{4.5x}{100}$ = 225

x = $\frac{22500}{4.5}$

x = 5000

The sum = Rs 5000

Answer 2

Step-by-step explanation:

Let the principle be Rs. 100 in both the cases

SI for 3½ or 7/2 years at 7%=P*R*T/100 =100*7*7/2/100

=49/2

=Rs.24.5

SI for 4 years at 5%=100*5*4/100

=Rs.20

The difference is=Rs.24.5-Rs.20

=Rs.4.5

If the difference is Rs.4.5,the principal=Rs.100

If the difference is Rs.225,the principal

=100/4.5*225

=100*10*225/45

=Rs.5000

so,Rs.5000 was the sum in both the cases

Hope it helps