Hello vaibhav101.

Let's see.

three partners X,Y,Z go into business. Originally X invests $2500, Y $3000 and Z $1500 after 7 months Y withdraws $1000 while ate the end of 8 months Z invests a further $2000. The total profits at the end of the year are $5568. How should profits be divided (in $)?

At the beginning the three partners invested:

X -------- 2500
Y -------- 3000
Z -------- 1500

A total of $7000.

This $7000 last for 7 months.

Then, Y withdraws $1000 and at the end of 8 months, Z invested $2000.

So, during the 1 month, the amount was 7000-1000 = $6000 and during the last 4 months, the amount was 6000+2000= $8000.

In conclusion, we have:

$7000 ------ 7 months
$6000 ------ 1 month
$8000 ------ 4 months

The total profits at the end of the year are $5568. If r represents the monthly rate, we have that $$7\cdot r\cdot7000+r\cdot6000+4\cdot r\cdot8000=5568$$ $$\Rightarrow\ \ 49000r+6000r+32000r=5568$$ $$\Rightarrow\ \ 87000r=5568\ \ \ \ \Rightarrow\ \ \ \ r=0.064.$$

Now, since X invested $2500 during 12 months, then his profit should be: $$X--\ 12\cdot0.064\cdot2500=1920.$$

Watching the answer choices, we can conclude that the correct answer is the option A.

Even though, let's calculate the profit of Y and Z.

Y invested $3000 during 7 months and $2000 during 5 months. Then his profit should be: $$Y--\ 7\cdot0.064\cdot3000\ +\ 5\cdot0.064\cdot2000=1344+640=1984.$$ Finally, Z invested $1500 during 8 months and $3500 during 4 months. Then his profit should be: $$Z--\ 8\cdot0.064\cdot1500\ +\ 4\cdot0.064\cdot3500=768+896=1664.$$ This proofs that the correct answer is the option A.

I hope it is clear enough.

I would like to see a shorter way to solve this PS question. <i class="em em-smiley"></i>