Question

A certain sum amounts to Rs.$17,700$ in $3$ years and Rs. $20,400$ in $6$ years under simple interest. Find the sum and rate of interest.

• A. $Rs.15,000,10$% p.a.
• B. $Rs.15,000,6$% p.a.
• C. $Rs.10,000,5$% p.a.
• D. $Rs.12,500,10$% p.a.

Answer 1

Answer: (B)

$Rs.15,000,6$% p.a.

Case 1 ($3$ years)

Amount $=17700$

Amount $=P+\frac{PRT}{100}$

$P+\frac{3PR}{100}=17700\to \left(1\right)$

Case 2 ($6$ years)

Amount $=20400$

$P+\frac{6PR}{100}=20400\to \left(2\right)$

$\left(2\right)-\left(1\right)$

$P-P+\frac{6PR}{100}-\frac{3PR}{100}=20400-17700=2700$

$\frac{3PR}{100}=2700\to \left(3\right)$

substituting $\left(3\right)in\left(1\right)$

$P+2700=17700$

$P=15000$

from $\left(3\right)$

$\frac{3\times 15000}{100}R=2700$

R $=6\%$

$\therefore$ sum $=15000$ , Rate $=6\%$ per annum.