X and Y can do a piece of work in 18 days and 27 days, respectively. Starting with X, they work on alternate days. The whole number of days to complete the work by X and Y is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 22.
X’s 1 day work = 1/18
Y’s 1 day work = 1/27
In 2 days (X + Y):
= 1/18 + 1/27 = (3 + 2)/54 = 5/54
Work in 10 such days (20 days) = (5/54) × 10 = 50/54
Remaining work = 1 − 50/54 = 4/54 = 2/27
21st day → X’s turn → does 1/18 work
Check: 1/18 > 2/27 → Yes
Let required fraction of day = x
x/18 = 2/27 → x = (2/27) × 18 = 4/3 days
So, total time = 20 full days + 4/3 day = 21⅓ days
Answer: 22 days (whole number of days required)