Question

A sum is invested for $3$ years compounded at $5\%,10\%$ and $20\%$ respectively. In three years, if the sum amounts to Rs. $16,632$, then find the sum.

• A. Rs. $11000$
• B. Rs. $12000$
• C. Rs. $13000$
• D. Rs. $14000$

Answer 1

Answer: (B)

Rs. $12000$

Let the original amount $=$ Rs. $100$.

In the first year, it increases by $5\%$.

$\therefore$ the amount after $1$ yr. $=$ Rs. $(100+100\times \frac{5}{100})=$ Rs. $105.$

In the second year, it increases by $10\%$.

$\therefore$ the amount after $2$ yr. $=$ Rs. $(105+105\times \frac{10}{100})=$ Rs. $\mathrm{115.5.}$

In the third year, it increases by $20\%$.

$\therefore$ the amount after $3$ yr. $=$ Rs. $(115.5+115.5\times \frac{20}{100})=$ Rs. $\mathrm{138.6.}$ $=138.6\%$ of Rs. $100$

$\therefore$ Rs. $138.6\%$ of the original money $=$ Rs. $16632$.

$\Rightarrow$ The original money $=$ Rs. $\frac{16632}{138.6}\times 100=$ Rs. $12000.$