At simple interest, a certain sum of money amounts to RS 1,250 in 2 years and to Rs 2,000 in 5 years. Find the rate of interest per annum (rounded off to two decimal places).

Explanation

To find the rate of interest per annum, we can use the information given about the amounts in 2 years and 5 years. Given: 1. The sum of money becomes Rs 1,250 in 2 years. 2. The sum of money becomes Rs 2,000 in 5 years. Step 1: Calculate the Interest for the Additional 3 Years The difference between the amounts in 5 years and 2 years is the interest earned in the additional 3 years. Interest for 3 years=2000−1250=750\text{Interest for 3 years} = 2000 - 1250 = 750Interest for 3 years=2000−1250=750 Step 2: Calculate the Annual Interest Since this interest is for 3 years, the interest per year is: Annual Interest=7503=250\text{Annual Interest} = \frac{750}{3} = 250Annual Interest=3750​=250 Step 3: Determine the Principal In 2 years, the total amount is Rs 1,250, and we know the annual interest is Rs 250. Therefore, the interest for 2 years is: Interest for 2 years=250×2=500\text{Interest for 2 years} = 250 \times 2 = 500Interest for 2 years=250×2=500 Now, we can find the principal (PPP) by subtracting the interest from the total amount in 2 years: P=1250−500=750P = 1250 - 500 = 750P=1250−500=750 Step 4: Calculate the Rate of Interest Now that we have the principal P=750P = 750P=750 and the annual interest =250= 250=250, we can use the simple interest formula to find the rate RRR: Simple Interest=P×R×T100\text{Simple Interest} = \frac{P \times R \times T} {100}Simple Interest=100P×R×T​ Since we know that the interest for 1 year is Rs 250, we can substitute: 250=750×R×1100250 = \frac{750 \times R \times 1}{100}250=100750×R×1​ Solving for RRR: R=250×100750=25000750=33.33R = \frac{250 \times 100}{750} = \frac{25000}{750} = 33.33R=750250×100​=75025000​=33.33 Answer: The rate of interest per annum is 33.33%.