Question

X and Y together can do a piece of work in 18 days. When Y and Z work together, they
can do the work in 12 days. But when X and Z work together, they can do the same piece
of work in 24 days. How many days will it take to complete the same work if all of them
work together?
A.6
B.7.5
C. 8
D. 9
E. None
​

Answer 1

Step-by-step explanation:

If X and Y can do a work in 10 days, it means that X and Y do (1/10)th of the work in a day.

If Y and Z can do a work in 12 days, it means that Y and Z do (1/12)th of the work in a day.

If X and Z can do a work in 15 days, it means that X and Z do (1/15)th of the work in a day.

So 2X + 2Y + 2Z = (1/10)+(1/12)+(1/15) = (6/60)+(5/60)+(4/60) = 15/60 or 1/4th of the work in a day, or X, Y and Z do 1/8th of the work in a day.

Z can do (1/8)-(1/10) = (5–4)/40 = 1/40th part in a day. So he will take 40 days to do the work himself.

X can do (1/8)-(1/12) = (3–2)/24 = 1/24th part in a day. So he will take 24 days to do the work himself.

Y can do (1/8)-(1/15) = (15–8)/120 = 7/120th part in a day. So he will take 17 and 1/7th of a day to do the work himself.

Check: X + Y + Z = (1/24)+(7/120)+(1/40) = (5+7+3)/120 = 15/120 = 1/8th of the work in a day. Correct.

X takes 24 days, Y takes 17 and 1/7th of a day,and Z takes 40 days to do the same work, working alone.

X and Y did a work in 12 days. Y and Z did the same work in 15 days and Z and X did this work in 20 days then in how many days X,Y and Z will do the work together?

X and Y can do a job in 10 days, Y and Z can do in 12 days and X and Z can do it in 15 days.