Question

In a business, $A$ invests $600$ rupees more than $B.$ The capital of $B$ remains invested for $7\frac{1}{2}$ months, while the capital of $A$ remains invested for $2$ more months. If the total profit be $620$ rupees and $B$ gets $140$ rupees less than what $A$ gets, then $A^{\prime }s$ capital is

• A. $2400$ rupees
• B. $2800$ rupees
• C. $3000$ rupees
• D. $3200$ rupees

Answer 1

The correct option is C $3000$ rupees

Let $B^{\prime }s$ capital be $x$ rupees.
Then, $A^{\prime }s$ capital $=(600+x)$ rupees
$\therefore A:B=\left(\right(x+600)\times \frac{19}{2}):(x\times \frac{15}{2})$
$=(19x+11400):15x$

$A^{\prime }s$ share $=(620\times \frac{19x+11400}{34x+11400})$
$B^{\prime }s$ share $=(620\times \frac{15x}{34x+11400})$

$\therefore 620(\frac{19x+11400}{34x+11400}-\frac{15x}{34x+11400})=140$
$\Rightarrow 62(4x+11400)=14(34x+11400)$
$\Rightarrow (476-248)x=(62-14)\times 11400$
$\Rightarrow 228x=48\times 11400$
$\Rightarrow x=\frac{48\times 11400}{228}=2400$
Hence $A^{\prime }s$ capital $=2400+600=3000$