X alone can complete a work in 56 days and Y alone can do it in 72 days. both completed in:

Given:
X's time = 56 days
Y's time = 72 days
Formula Used:
Combined time = $$\frac{X \times Y}{X + Y}$$​​
Solution:
​$$Time = \frac{56 \times 72}{56 + 72} = \frac{56 \times 72}{128}\\ \ \\Time = \frac{7 \times 72}{16} = \frac{7 \times 9}{2} = 31.5 days$$​​
So the correct answer is (a).

OR

Solution:
Work done by X in 1 day = 1/56

Work done by Y in 1 day = 1/72

Total work done in 1 day

1/56 + 1/72

LCM of 56 and 72 = 504

= 9/504 + 7/504

= 16/504

= 2/63

Total time

T = 63/2 = 31.5 days

Final Answer = 31.5 days