Rs. 6000 was lent partly @ 5% and partly @ 7% simple interest. The total interest received after 4 years is Rs. 1600. What is the amount lent @ 5% SI?

Question

Question

This question was previously asked in

MP Excise Constable Official Paper (Held On: 26 Feb 2023 Shift 1)

Answer 1

Given:

Total sum lent = ₹6000

Part lent at 5% simple interest.

Part lent at 7% simple interest.

Total interest received after 4 years = ₹1600

Formula Used:

Simple Interest (SI) = (Principal (P) × Rate (r) × Time (t)) / 100

Calculations:

Let the amount lent at 5% be ₹x.

Then the amount lent at 7% will be ₹(6000 - x).

Simple interest received from the amount lent at 5% after 4 years:

SI₁ = (x × 5 × 4) / 100 = 20x / 100 = 0.2x

Simple interest received from the amount lent at 7% after 4 years:

SI₂ = ((6000 - x) × 7 × 4) / 100 = (28 × (6000 - x)) / 100 = (168000 - 28x) / 100 = 1680 - 0.28x

The total interest received is ₹1600.

SI₁ + SI₂ = 1600

0.2x + (1680 - 0.28x) = 1600

0.2x + 1680 - 0.28x = 1600

1680 - 0.08x = 1600

1680 - 1600 = 0.08x

80 = 0.08x

x = 80 / 0.08

x = 8000 / 8

x = 1000

So, the amount lent at 5% simple interest is ₹1000.

∴ The amount lent @ 5% SI is ₹1000.

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