At what rate the simple interest will be \(\dfrac{2}{5}\) times to the original sum in 10 years ?
4%
Simple interest is \(\text{SI} = \dfrac{P \times R \times T}{100}\), where P is the principal, R the rate per cent per annum and T the time in years.
Step 1 — The interest equals \(\dfrac{2}{5}\) of the sum, so \(\text{SI} = \dfrac{2P}{5}\) with T = 10 years.
Step 2 — \(\dfrac{2P}{5} = \dfrac{P \times R \times 10}{100}\), which gives \(R = \dfrac{2 \times 100}{5 \times 10} = 4\).
A rate of 6% would give interest of 60% of the sum in 10 years, and the two fractional rates give about 55% and 67%, all larger than the required 40%.
4% option is correct.
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