A and B can complete a piece of work in 25 days and 55 days, respectively. The total number of days (in whole number) to complete the work, if A and B both work together, is:

Let the total work be the Least Common Multiple (LCM) of 25 and 55.
LCM(25,55)=275 units
Now, let's find their individual efficiencies (work done per day):

Efficiency of A =
25
275
​
=11 units/day

Efficiency of B =
55
275
​
=5 units/day

Combined efficiency of A and B working together:

Combined Efficiency=11+5=16 units/day
Total days required to complete the work together:

Time=
Combined Efficiency
Total Work
​
=
16
275
​
=17.1875 days
Rounding to the nearest whole number as specified in the options, the value is approximately 17 or 18. Let's re-verify the closest option from the choices provided:

16
275
​
≈17.18≈17
Since 17 is not an option, let's look at the closest whole number available in the multiple-choice list:
Option C is 18.