# Difficult Ratios & Proportion Solved QuestionAptitude Discussion

 Q. $A$ and $B$ enter in to a partnership and $A$ invests Rs. 10,000 in the partnership. At the end of 4 months he withdraws Rs.2000. At the end of another 5 months, he withdraws another Rs.3000. If $B$ receives Rs.9600 as his share of the total profit of Rs.19,100 for the year, how much did $B$ invest in the company?
 ✖ A. Rs. 12,000 ✔ B. Rs. 8,000 ✖ C. Rs. 6,000 ✖ D. Rs. 96,000

Solution:
Option(B) is correct

The total profit for the year is 19100. Of this $B$ gets Rs.9600. Therefore, $A$ would get $(19100 - 9600)$ $= \text{Rs. }9500$

The partners split their profits in the ratio of their investments.

Therefore, the ratio of the investments of,

$A : B = 9500 : 9600 = 95 : 96.$

$A$ invested Rs.10000 initially for a period of 4 months. Then, he withdrew Rs.2000.

Hence, his investment has reduced to Rs.8000 (for the next 5 months).

Then he withdraws another Rs.3000. Hence, his investment will stand reduced to Rs.5000 during the last three months.

So, the amount of money that he had invested in the company on a money-month basis will be,

$= 4 \times 10000 + 5 \times 8000 + 3 \times 5000$

$= 40000 + 40000 + 15000$

$= 95000$

If $A$ had 95000 money months invested in the company, $B$ would have had 96,000 money months invested in the company (as the ratio of their investments is $95 : 96$).

If $B$ had 96,000 money-months invested in the company, he has essentially invested $\dfrac{96000}{12} = \textbf{Rs. 8000}$