A certain amount of money at simple interest amounts to ₹ 1,404 in 2 years and to ₹ 1,560 in 5 years. What is the rate of simple interest per annum ?

Correct option is B

Given:

Amount after 2 years = ₹1,404

Amount after 5 years = ₹1,560

Time periods = 2 years and 5 years

Formula Used:

Simple Interest (S.I.) = $$\frac{{P \times R \times T}}{{100}}$$​, where (P) is the principal, (R) is the rate, and (T) is the time.

Amount (A) = Principal (P) + Simple Interest (S.I.).

Solution:

The difference in amounts after 5 years and 2 years is the simple interest for the 3 years (5 years - 2 years).

Difference in amounts = ₹1,560 - ₹1,404 = ₹156.

Therefore, the simple interest for 3 years = ₹156.

Simple interest for 1 year = $$\frac{{156}}{{3}} = ₹52$$​​

The simple interest for 2 years is ₹52 × 2 = ₹104. Since the amount after 2 years is ₹1,404, we can calculate the principal:

Principal = ₹1,404 - ₹104 = ₹1,300.

For 2 years, the simple interest is ₹104. 
​$$104 = \frac{{1300 \times R \times 2}}{{100}}$$​​

104 =$$\frac{{2600 \times R}}{{100}}$$​​
10$$4 \times 100 = 2600 \times R$$​​
10400 = 2600R
R =$$\frac{{10400}}{{2600}} =$$​ 4%
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