Question

Two equal sums of money were lent at simple interest at 10% per annum for 3 years and 4 years, respectively. If the difference in the interests for the two periods was ₹450, then how much is each sum?​

Answer 1

Given that:

• Two equal sums of money were lent at simple interest at 10% per annum.

Let us assume:

• Each sum of money be P.

We know that:

• SI = PRT/100

Where,

• SI = Simple interest
• P = Sum of money
• R = Rate
• T = Time

We have:

• Sum of money = P
• Rate = 10% p.a.

Simple interest for 3 years:

↠ SI₁ = (P × 10 × 3)/100

↠ SI₁ = P × 3/10

↠ SI₁ = P × 0.3

↠ SI₁ = 0.3P

Simple interest for 4 years:

↠ SI₂ = (P × 10 × 4)/100

↠ SI₂ = P × 4/10

↠ SI₂ = P × 0.4

↠ SI₂ = 0.4P

The difference in the interests for the two periods was ₹450.

↠ SI₂ - SI₁ = 450

Putting the values.

↠ 0.4P - 0.3P = 450

↠ 0.1P = 450

↠ P = 450/0.1

↠ P = 4500

Hence,

• Each sum is ₹4500.