Question

A began a business with Rs 45000 and was joined afterwards by B with Rs 54000. After how many months did B join, if the profits at the end of the year were divided in the ratio 2:1?

• A. 4
• B. 5
• C. 6
• D. 7
• E. None of the above

Answer 1

The correct option is D 7

Suppose B joined after x months
$\therefore \frac{45000\times 12}{54000\times (12-x)}=\frac{2}{1}$
$\Rightarrow 45000\times 12$
$=54000\times 12\times 2-54000\times 2\times x$
$\Rightarrow 108x=54\times 24-45\times 12$
$\Rightarrow 27x=54\times 6-45\times 3$
$\Rightarrow 27x=324-135=189\Rightarrow x=7$
$\therefore$ B joined after 7 months