Question

A sum of money at simple interest amounts to rs.854 in 4 years and to rs.893 in 5 years. The sum is

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 = 4 years and Rate of Interest is R %

I₁ = (S × 4 × R)/100 = 4SR/100

Amounted sum = Rs. 854

⇒ S + I₁ = 854

⇒ S + (4SR/100) = 854

⇒ (100S + 4SR)/100 = 854

⇒ 100S + 4SR = 85400 .....(i)

Case 2.

In this case, T = 5 years and Rate of Interest is R %

I₂ = (S × 5 × R)/100 = 5SR/100

Amounted sum = Rs. 893

⇒ S + I₂ = 893

⇒ S + (5SR/100) = 893

⇒ (100S + 5SR)/100 = 893

⇒ 100S + 5SR = 89300 .....(ii)

Computations :

Now, {(i) × 5} - {(ii) × 4} ⇒

5 (100S + 4SR) - 4 (100S + 5SR)

= 5 (85400) - 4 (89300)

⇒ 500S + 20SR - 400S - 20SR

= 427000 - 357200

⇒ 100S = 69800

⇒ S = 698

∴ the required sum is Rs. 698