Question

X and Y entered into partnership with Rs. 700 and Rs. 600 respectively. After 3 months, X withdrew \( \frac{2}{7} \) of his stock but after 3 months, he puts back \( \frac{3}{5} \) of what he had withdrawn. The profit at the end of the year is Rs. 726. How much of this should X receive?

• A. Rs. 336
• B. Rs. 366
• C. Rs. 633
• D. Rs. 663

Hint:

For partnership problems, compute time-weighted contributions separately before computing profit shares.

Answer 1

The Correct Option is B

X’s initial capital = Rs. 700, Y’s capital = Rs. 600
For the first 3 months, X’s investment remains Rs. 700.
After 3 months, X withdraws \( \frac{2}{7} \) of 700: \[ \frac{2}{7} \times 700 = 200 \] Remaining capital: \[ 700 - 200 = 500 \] After another 3 months, X puts back \( \frac{3}{5} \) of what he withdrew: \[ \frac{3}{5} \times 200 = 120 \] New capital: \[ 500 + 120 = 620 \] Investment time-weighted: \[ 700 \times 3 + 500 \times 3 + 620 \times 6 = 2100 + 1500 + 3720 = 7320 \] Y’s total contribution: \[ 600 \times 12 = 7200 \] Ratio of profit division: \[ \frac{7320}{7320 + 7200} \times 726 = \frac{7320}{14520} \times 726 \] \[ X's \text{ share} = 366 \] Thus, X should receive Rs. 366.