A certain sum of money becomes Rs. 1000 in 2 years and Rs. 1100 in 4 years at simple rate of interest. The rate of interest per annum is
$5 \frac{5}{9}$ %
The defining feature of simple interest is that the same fixed amount of interest is earned in every equal time period, because interest is always calculated on the original principal and never on accumulated interest. This makes the amount grow in a straight line over time.
The sum becomes Rs. 1000 after 2 years and Rs. 1100 after 4 years. The extra 2 years (from year 2 to year 4) added Rs. 1100 minus Rs. 1000 = Rs. 100 of interest. Since interest is uniform under simple interest, this Rs. 100 corresponds to 2 years, so the interest for one year is Rs. 50.
To find the principal, subtract the interest earned in the first 2 years (which is also Rs. 100) from the amount at the end of 2 years: Principal = Rs. 1000 minus Rs. 100 = Rs. 900.
The rate per annum is then (annual interest divided by principal) times 100 = (50 divided by 900) times 100 = 5000/900 = 50/9 = 5 5/9 %.
The other options come from wrong choices of principal or interest — for example, treating Rs. 1000 itself as the principal, or using the wrong number of years for the interest gap. Working strictly from the two equal-length intervals gives the correct rate of 5 5/9 % per annum.
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