A sum of money at simple interest amounts to Rs.1,012 in 2$1/2$ years and to Rs.

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A sum of money at simple interest amounts to Rs.1,012 in 2$1/2$ years and to Rs.1,067.20 in 4 years. The rate of interest per annum is :

Options:

A . 3%

B . 2.5%

C . 5%

D . 4%

Answer: Option D
Answer: (d)Principal + S.I. for $5/2$ years = Rs.1012 ...(i)Principal + S.I. for 4 years = Rs.1067.20 ...(ii)Subtracting equation (i) from (ii)S.I. for $3/2$ years = Rs.55.20S.I. for $5/2$ years= $55.20 × 2/3 × 5/2$ = Rs.92Principal= Rs.(1012 - 92) = Rs.920Rate = ${92 × 100}/{920 × 5/2}$= ${2 × 92 × 100}/{920 × 5}$ = 4%Using Rule 12,R = $({A_1 - A_2}/{A_2T_1 - A_1T_2})$ × 100= $({1012 - 1067.20}/{1067.20 × 5/2 - 1012 × 4}) × 100$= ${- 55.2}/({2668 - 4048}) × 100$= ${- 55.2}/{- 1380} × 100$ = 4%

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