15 men or 20 women can complete a task in 108 (1/3) days, while 25 men and 75 women together can complete it in P days

Q. 15 men or 20 women can complete a task in 108 (1/3) days, while 25 men and 75 women together can complete it in P days. Deepak can do an assignment in (1.5P – 10) days, while Deepa can do the same assignment in 0.8P days. They started the work together and after Q days Deepak left, the remaining assignment completed by Deepa in 7 days. Find the value of P is how much percentage more or less than that of Q.

A.400%

B.250%

C.300%

D.200%

E. None of these

Sol:

Let efficiency of a man and a woman = a
units/day and b units/day respectively.
Now, 15a x 325/3 = 20b x 325/3
So, a/b = 4/3
So, total work = 15 x 4 x 325/3 = 6500 units
So, value of P = 6500 / (25 x 4 + 75 x 3) = 20
days
Now, time taken by Deepak to complete the
assignment = 1.5 x 20 – 10 = 20 days
Time taken by Deepa = 80% of 20 = 16 days
Let the total work = 80
Efficiency of Deepak = 80/20 = 4 units/day
Efficiency of Deepa = 80/16 = 5 units/day
Now,
(4 + 5) x Q + 5 x 7 = 80
9Q = 45

So, value of Q = 45/9 = 5 days
Required percentage change = (20 – 5)/5 x 100
= 300%
Hence answer is option C