Compound Interest Ques 3

Question

The respective ratio of the sums invested for 2 years each, in scheme A offering $20 \%$ per annum compound interest (compounded annually) and in Scheme B offering $9\%$ p.a. simple interest is $1: 3$. Difference between the interests earned from both the schemes is Rs. 12000 . How much was invested in scheme A ?

(1) Rs. 10500

(2) Rs. 15000

(3) Rs. 12000

(4) Rs. 12500

(5) Rs. 10000

(IBPS Bank PO/MT CWE-V (Preliminary) 10.10.2015)

Show Answer

Answer: (3)

Solution: (3)

Amount invested in scheme A = Rs. $x$ (let)

Amount invested in scheme B = Rs. $3 x$

C.I. obtained from scheme A

$=P\left[\left(1+\frac{R}{100}\right)^{T}-1\right]$

$=Rs. $ $x\left[\left(1+\frac{20}{100}\right)^{2}-1\right]$

$=$ Rs. $x\left[\left(1+\frac{1}{5}\right)^{2}-1\right]$

$=$ Rs. $x\left[\left(\frac{6}{5}\right)^{2}-1\right]$

$=$ Rs. $x\left(\frac{36}{25}-1\right)=$ Rs. $\left(\frac{11 x}{25}\right)$

S.I. from scheme B $=\frac{\text { Principal } \times \text { Time } \times \text { Rate }}{100}$

$=\frac{3 x \times 2 \times 9}{100}=$ Rs. $\frac{54 x}{100}$

$\therefore \frac{54 x}{100}-\frac{11 x}{25}=1200$

$\Rightarrow \frac{54 x-44 x}{100}=1200$

$\Rightarrow \frac{10 x}{100}=1200$

$\Rightarrow x=1200 \times 10=$ Rs. 12000