Question : A sum of Rs. 600 becomes Rs. 840 at simple interest in 4 years. In how many years will the sum of Rs. 1500 amount to Rs. 2100 at the same rate of simple interest?
Option 1: 5 years
Option 2: 4 years
Option 3: 2 years
Option 4: 3 years
Correct Answer: 4 years
Solution :
Given,
P = Rs. 600, A = Rs. 840, and T = 4 years,
Simple interest, SI = Amount – Principal
we can find the rate of interest (R):
⇒ R = $\frac{SI×100}{P×T}$
⇒ R = $\frac{840−600}{600×4}×100$
⇒ R = $\frac{240}{2400}×100$
⇒ R = 10%
Now, we can use this rate of interest to find the time (T′) for the new principal (P′) and amount (A′).
A′ = P′ + SI′ and SI′ = P′ × R × T′
Given,
P′ = Rs.1500 and A′ = Rs. 2100
Let the time be T'.
And, T′= $\frac{SI'×100}{P′ × R}$
⇒ T′ = $\frac{2100−1500}{1500×10}×100$
⇒ T′ = $\frac{600}{15000}×100$
⇒ T′ = 4 years
Hence, the correct answer is 4 years.
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