Question

q: a, b, and c can complete a piece of work in 20, 30, and 60 days respectively. if a works every day, and is assisted by b and c on alternate days (starting with b), in how many days will the work be completed?
a. 12.00 days
b. 13.25 days
c. 14.50 days
d. 15.00 days

Explanation:

Step1: Calculate work - rate per day

Let the total work be 60 units (LCM of 20, 30, 60). The work - rate of A is $\frac{60}{20}=3$ units per day, the work - rate of B is $\frac{60}{30}=2$ units per day, and the work - rate of C is $\frac{60}{60}=1$ unit per day.

Step2: Calculate work done in 2 - day cycle

In the first day, A and B work together, and the work done is $3 + 2=5$ units. In the second day, A and C work together, and the work done is $3+1 = 4$ units. So, in a 2 - day cycle, the work done is $5 + 4=9$ units.

Step3: Calculate number of 2 - day cycles

Let the number of 2 - day cycles be $n$. After $n$ 2 - day cycles, the work done is $9n$ units. We want to find $n$ such that $9n\leq60$. When $n = 6$ (i.e., 12 days), the work done is $9\times6 = 54$ units.

Step4: Calculate remaining work and time to complete it

After 12 days, the remaining work is $60−54 = 6$ units. On the 13th day, A and B work together. Since their combined work - rate is $3 + 2=5$ units per day, after the 13th day, the remaining work is $6−5 = 1$ unit. On the 14th day, A and C work together. Since their combined work - rate is $3 + 1=4$ units per day, the time taken to complete the remaining 1 unit is $\frac{1}{4}=0.25$ days.
So, the total number of days to complete the work is $13 + 0.25=13.25$ days.

Answer:

B. 13.25 days