Question

The simple interest on a certain sum for 8 years at 12 per cent per annum is ₹ 3120 more than the simple interest on the same sum for 5 years at 14 per cent per annum. Find the sum.

Answer 1

Given, I₁ – I₂ = ₹ 3120

T₁ = 8 yr, R₁ = 12%

T₂ = 5 yr, R₂ = 14%

And P₁ = P₂ = P

According to the question,

I₁ – I₂ = ₹ 3120

⇒ `(P_1 xx R_1 xx T_1)/100 - (P_2 xx R_2 xx T_2)/100` = 3120

⇒ `(P xx 12 xx 8)/100 - (P xx 14 xx 5)/100` = 3120

⇒ `P/100 [12 xx 8 - 14 xx 5]` = 3120

⇒ P[96 – 70] = 3120 × 100

⇒ 26P = 312000

⇒ P = `312000/26`

∴ P = ₹ 12000

Hence, the sum is ₹ 12000.