To do a certain work, Q and R work on alternate days, with Q beginning the work on the first day. Q can finish the work alone in 56 days. If the work gets completed in 37.5 days, then R alone can finish half of the same work in:

Correct option is C

Given:

Q can finish the work alone in 56 days

Q and R work on alternate days, starting with Q

Total work is completed in 37.5 days

Need to find the number of days R alone will take to complete half the work

Formula Used:

Efficiency = $$\frac{\text{Work}}{\text{Time taken}}$$​​

Solution:

Let total work = LCM of 56 = 56 units

Q's 1-day work = $$\frac{56}{56}$$​ = 1 unit/day

Let R's 1-day work = r units/day

In 37.5 days, the number of days worked by Q = 19 days (odd days)

Number of days worked by R = 18.5 days (even days)

Now, total work done:

19 days by Q => 19 × 1 = 19 units

18.5 days by R => 18.5 × r units

Total work = 56 units

19 + 18.5r = 56

18.5r = 37

r =$$\frac{37}{18.5}$$​ = 2 units/day

So, R alone can do 2 units/day.

Days taken by R to complete half of total work

​$$= \frac{28}{2} = 14 \text{ days}$$​​