A sum on simple interest at the rate of 5% per annum amounts to ₹4,160 in 6 years. Find the sum.

Correct option is C

Given:
Amount (A) = ₹4160
Rate of interest (R) = 5% per annum
Time (T) = 6 years
​Formula Used:
A = P + $$\frac{P \times R \times T}{100}$$​

where A is the amount, P is the principal (sum), R is the rate, and T is the time.

Solution:
Substitute the given values into the formula:
4160 = P + $$\frac{P \times 5 \times 6}{100}$$ 

$$4160 = P + \frac{30P}{100}$$​​

4160 = P $$\left( 1 + \frac{30}{100} \right)$$​​

4160 = P $$\times \left( \frac{130}{100}\right)$$​​

4160 = $$P \times 1.3$$​​

P = $$\frac{4160}{1.3} = 3200$$​​

Thus, the correct option is (c)  ₹3,200

Alternate Method:

Let, Principal = 100%

Simple Interest for 6 years = 6 $$\times$$ 5 % = 30 %

Amount = Principal + SI

Amount = 100%  + 30% = 130%

Principal = $$\frac{4160}{130\%}\times 100\%$$ = ₹3,200​

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