Question

The number of days required by A, B and C to work individually is 6, 12 and 8 respectively. They started a work doing it alternatively. If A has started then followed by B and so on, how many days are needed to complete the whole work?

• A. 8
• B. 7.5
• C. 8.5
• D. $9\frac{1}{2}$

Answer 1

The correct option is A 8


In 3 days A, B, C do $\frac{3}{8}$ work
in 6 days A, B, C do $\frac{3}{4}$ work
Rest work = $\frac{1}{4}$ which is less than $\frac{3}{8}$
On the 7th day, $\frac{1}{6}$ more work will be done by A
Now rest work $\frac{1}{4}-\frac{1}{6}=\frac{1}{12}$
Now, this rest work $\left(\frac{1}{12}\right)$ will be done by B in 1 complete day.
Thus, total number of days = 6 + 1+ 1= 8 days

Alternate Method:
Efficiency of A = 16.66%
Efficiency of B = 8.33%
Efficiency of C = 12.5%
Efficiency of A + B = 25%
Efficiency of A + B+C = 37.5%
In 3 days A, B, C completes 37.5% work
In 6 days A, B, C completes 75% work
This 25% work will be completed by A and B in next 2 days
Thus total 6 + 2 = 8 days are needed