X can do a job in 20 days, Y in 30 days and Z in 36 days. Y and Z begin the work but have to leave after 5 days. How many complete number of days will X take to finish the remaining job?

Correct option is A

Given:
X can do the job in 20 days
Y can do the job in 30 days
Z can do the job in 36 days
Y and Z work together for 5 days and then leave
Formula Used:
Total Work = LCM of (Time taken by X, Y, Z)
Work rate = Total Work ÷ Time
Time = Remaining Work ÷ Rate
Solution:
Total work = LCM of 20, 30, 36 = 180
1-day work of each:
X’s 1-day work = 180 ÷ 20 = 9 units/day
Y’s 1-day work = 180 ÷ 30 = 6 units/day
Z’s 1-day work = 180 ÷ 36 = 5 units/day
Work done by Y and Z in 5 days:
Y + Z in 1 day = 6 + 5 = 11 units
In 5 days: 11 × 5 = 55 units
Remaining work = 180 − 55 = 125 units
Time taken by X to finish remaining work:
X’s 1-day work = 9 units
Time = 125 ÷ 9 = 13 remainder 8
In 13 days, X does 13 × 9 = 117 units
Work left = 125 − 117 = 8 units
So, X needs 1 more complete day to finish the remaining work.
Therefore, total complete days = 13 + 1 = 14 days