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

1Rs. 110, Rs. 220, Rs. 336
2Rs. 112, Rs. 223, Rs. 336
3Rs. 105, Rs. 223, Rs. 330
4None of these

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Remainder \\ = Rs . [671 + (3 + 7 + 9)] \\ = Rs . 690. \\ A's share \\ = Rs . [(690 \times \frac{1}{6}) - 3] \\ = Rs . 112. \\ B's share \\ = Rs . [(690 \times \frac{2}{6}) - 7] \\ = Rs . 223. \\ C's share \\ = Rs . [(690 \times \frac{3}{6}) - 9] \\ = Rs . 336. \end{aligned}

$\eqalign{ & {\text{Remainder}} \cr & = {\text{Rs}}{\text{.}}\left[ {671 + \left( {3 + 7 + 9} \right)} \right] \cr & = {\text{Rs}}{\text{. }}690. \cr & {\text{A's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{1}{6}} \right) - 3} \right] \cr & = {\text{Rs}}{\text{. }}112. \cr & {\text{B's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{2}{6}} \right) - 7} \right] \cr & = {\text{Rs}}{\text{. }}223. \cr & {\text{C's share}} \cr & = {\text{Rs}}{\text{.}}\left[ {\left( {690 \times \frac{3}{6}} \right) - 9} \right] \cr & = {\text{Rs}}{\text{. }}336. \cr}$