Divide $₹$671 among A, B, C such that if their shares be increased by $₹$3, $₹$7 and $₹$9 respectively, the remainder shall be in the ratio 1 : 2: 3

Let A's share be $\text{ ₹ }$ x, 

B's share be$\text{ ₹ }$y. 

Then, C's share =$\text{ ₹ }$ [671-(x +y)]

Now $x+3:y+7:671-(x+y)+9=1:2:3$

$\begin{array}{l}\Rightarrow x+3:y+7:680-(x+y)=1:2:3\\ \therefore x+3=\frac{1}{6}\times 690=115\\ \Rightarrow x=₹112\end{array}$

Also, $y+7=\frac{2}{6}\times 690=230$

$\Rightarrow y=₹223$

$\therefore$ C's share $=\mathrm{Rs}[671-(112+223\left)\right]=\mathrm{Rs}336$