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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.
Solution
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.
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