Question

A starts a business with Rs.$40,000$. After $2$ months, $B$ joined him with Rs. $60,000$. $C$ joined them after some more time with Rs. $1,20,000$. At the end of the year, out of a total profit of Rs. $3,75,000$, $C$ gets Rs. $1,50,000$ as his share. How many months after $B$ joined the business, did $C$ join?

Answer 1

Let $C$ joined for $x$ months

Ratios of their investment,

$=40000\times 12:60000\times 10:120000\times x$

$=40\times 12:60\times 10:120\times x$

$=40:5\times 10:10\times x$

$=8:10:2x$

$=4:5:x$

$C^{\prime }$s share $=150000$

$\Rightarrow \frac{375000x}{9+x}=150000$

$\Rightarrow 375x9+x=150$

$\Rightarrow 375x=1350+150x$

$\Rightarrow 225x=1350$

$\Rightarrow x=6$

Thus $C$ joined for $6$ months.

Total months $B$ joined $=10$

Thus $C$ joined after $B=10-6=4$ month