Question

David invested certain amount in three different schemes $A,B$ and $C$ with the rate of interest $10\%$ p.a., $12\%$ p.a,m and $15\%$ p.a, respectively. If the total interest accured in one year was Rs. $3200$ and the amount invested in Scheme $C$ was $150\%$ of the amount invested in Scheme $A$ and $240\%$ of the amount invested in Scheme $B$, what was the amount invested in scheme $B$?

• A. Rs. $5000$
• B. Rs. $6500$
• C. Rs. $6000$
• D. Rs. $8000$

Answer 1

Answer: (A)

Rs. $5000$

Let $x,y$ and $z$ be the amounts invested in schemes $A,B$ and $C$ respectively.

Then, $\left(\frac{x\times 10\times 1}{100}\right)+\left(\frac{y\times 12\times 1}{100}\right)+\left(\frac{z\times 15\times 1}{100}\right)=3200$
$\Rightarrow 10x+12y+15z=320000$ ..........(i)
Given, $z=240\%$ of $y=$ $\frac{240}{100}\times y=\frac{12}{5}y$ ..........(ii)
and $z=150\%$ of $x=$$\frac{150}{100}\times x=\frac{3}{2}x$
$\Rightarrow x=\frac{2}{3}z=\frac{2}{3}\times \frac{12}{5}y=\frac{8}{5}y$ ..........(iii)
From (i), (ii) and (iii), we have
$10\times \frac{8}{5}y+12y+15\times \frac{12}{5}y=320000$
$\Rightarrow 16y+12y+36y=320000\Rightarrow 64y=320000$
$\Rightarrow y=\frac{320000}{64}=5000$
$\therefore$ sum invested in scheme $B=$ Rs. $5000$