### Question 12

SSC-CGL 2020 Mar 3 Shift 1

Re 4300 becomes Re 4644 when invested at SI for 2 years. What will Re 10104 become when invested for 5 years at the same plan?

### Solution in Brief

If simple rate of interest remains same, money-years are directly proportional to the interest earned.

Given that money-years of (4300 x 2 = 8600) yield an interest of (4644 - 4300) = 344 Rs.

By unitary method, (10104 x 5) will yield an interest of 344/8600 x (10104 x 5) = 2020.8, giving the final amount as 10104 + 2020.8 = 12124.8 Rs. ans!

### Solution in Detail

for case I: $\displaystyle I_1 = 4644 - 4300 = 344$

Also, $\displaystyle P_1 = 4300$, $\displaystyle T_1 = 2$ yrs.

By SI formula $\displaystyle I = P \times R \times T$

$\displaystyle \therefore 344 = 4300 \times R \times 2\text{ . . . (1)}$

for case II: $\displaystyle P_2 = 10104$, $\displaystyle T_2 = 5$

$\displaystyle \therefore I_2 = 10104 \times R \times 5\text{ . . . (2)}$

Divide (2) by (1) to get

$\displaystyle \frac{I_2}{344} = \frac{10104 \times R \times 5}{4300 \times R \times 2}$

$\displaystyle \implies I_2 = 2020.8$

$\displaystyle \therefore $ amount = $\displaystyle 10104 + 2020.8 $

$\displaystyle = \text{Rs. }12124.8\:\underline{ Ans}$

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