Alligation Or Mixture Ques 5
Question
$A$ and $B$ started a small business. $B$ invested Rs. 600 more than $A$. At the end of nine months from the start of the business, $B$ doubles his investment. If at the end of the year, the total profit earned was Rs. 13,800 and $A’s$ share in the profit was Rs. 4,800 what was $A’s$ investment?
(1) Rs. 1,500
(2) Rs. 1,800
(3) Rs. 1,200
(4) Rs. 900
(5) Rs. 1,000
(Bank of Maharashtra PO Exam, 26.10.2016)
Show Answer
Answer: (3)
Solution: (3)
$A’s$ investment = Rs. $x$ (let)
$\therefore$ $B’s$ investment $=$ Rs. $(x+600)$
Ratio of the equivalent capitals of $A$ and $B$ for 1 month
$=x \times 12:(x+600) \times 9+(2x + 1200) \times 3$
$=12 x: 9 x+5400+6 x+3600$
$=12 x: 15 x+9000$
$=4 x: 5 x+3000$
Sum of the terms of ratio $=4 x+5 x+3000=9 x+3000$
$\therefore$ $A’s$ share $=\left(\frac{4 x}{9 x+3000}\right) \times 13800$
$\Rightarrow\left(\frac{4 x}{9 x+3000}\right) \times 13800$ $=4800$
$\Rightarrow \frac{4 x}{9 x+3000}=\frac{4800}{13800}=\frac{8}{23}$
$\Rightarrow 72 x+24000=92 x$
$\Rightarrow 92 x-72 x=24000$
$\Rightarrow 20 x=24000$
$\Rightarrow x=\frac{24000}{20}=$ Rs. 1200
BETA
