Question

A certain sum amounts to rupees 10032 in 2yrs and rs 11248 in 3yrs at simple interest find the sum

Answer 1

Considerations :

• Sum = Rs. S
• Time = T years
• Rate of Interest = R %
• Interest = Rs. I

Formula :

I = ( S × T × R )/100

Case 1.

In this case, T = 2 years and Rate of Interest is R %

I₁ = (S × 2 × R)/100 = 2SR/100

Amounted sum = Rs. 10032

⇒ S + I₁ = 10032

⇒ S + (2SR/100) = 10032

⇒ (100S + 2SR)/100 = 10032

⇒ 100S + 2SR = 1003200 .....(i)

Case 2.

In this case, T = 3 years and Rate of Interest is R %

I₂ = (S × 3 × R)/100 = 3SR/100

Amounted sum = Rs. 11248

⇒ S + I₂ = 11248

⇒ S + (3SR/100) = 11248

⇒ (100S + 3SR)/100 = 11248

⇒ 100S + 3SR = 1124800 .....(ii)

Computations :

Now, {(i) × 3} - {(ii) × 2} ⇒

3 (100S + 2SR) - 2 (100S + 3SR)

= 3 (1003200) - 2 (1124800)

⇒ 300S + 6SR - 200S - 6SR

= 3009600 - 2249600

⇒ 100S = 760000

⇒ S = 7600

∴ the required sum is Rs. 7600