Question

X and Y can complete a piece of work in 8 days and 12 days, repectively. If they work on alternate days, with X working on the first day , how long will it take the duo to complete the same work?

• A. $$9\frac{2}{5}days$$
• B. $$9\frac{3}{5}days$$
• C. $$9\frac{2}{3}days$$
• D. $$9\frac{1}{2}days$$

Answer 1

Answer:

$$9\frac{1}{2}days$$

X can do the work in 8 days

Y can do the work in 12 days

LCM of 8 , 12 is 24

Total work =24

.Efiiciency of X = $\frac{24}{8}=3$

Efficiency of Y = $\frac{24}{12}=2$

Working on alternate days start with X

3+2 = 5 work done on 2days

in 4days 10 work done

in 6 days 15 work done

in 8days 20 work done

in 9days 23 work done

Remaining 1 work done by Y

$9+\frac{1}{2}=9\frac{1}{2}days$