Question

The number of days to finish a work by A is double the number of days to finish the work by B. The number of days to finish the work by C is half the number of days to finish the work by B. A can finish the work in 12 days. If B works on the 1st day, A works on the 2nd day and C works on the 3rd day, again B works on the 4th day and so on, then the work is finished in ______ days.

• A. 5.5
• B. 5.75
• C. 5
• D. 5.25

Answer 1

Answer:

A. 5.5

Let number of days taken by B = x

Then:

• A takes double → (A = 2x)

• C takes half → (C = \frac{x}{2})

Given: A takes 12 days
$2x = 12 \Rightarrow x = 6$

So:

• A = 12 days → work/day = ( \frac{1}{12} )

• B = 6 days → work/day = ( \frac{1}{6} )

• C = 3 days → work/day = ( \frac{1}{3} )

  Work done in 3-day cycle (B, A, C):

$\frac{1}{6} + \frac{1}{12} + \frac{1}{3}$
LCM = 12:
$= \frac{2 + 1 + 4}{12} = \frac{7}{12}$
After 3 days → work done = $( \frac{7}{12} )$

Remaining work:
$1 - \frac{7}{12} = \frac{5}{12}$
Day 4 (B works):

$\frac{5}{12} - \frac{1}{6} = \frac{5}{12} - \frac{2}{12} = \frac{3}{12} = \frac{1}{4}$
Day 5 (A works):

$\frac{1}{4} - \frac{1}{12} = \frac{3}{12} - \frac{1}{12} = \frac{2}{12} = \frac{1}{6}$
Day 6 (C works):

$\frac{1}{6} - \frac{1}{3} \Rightarrow \text{work finishes}$

C completes the remaining work in:

$\frac{\frac{1}{6}}{\frac{1}{3}} = \frac{1}{2} \text{ day}$

Total time:

$5 + \frac{1}{2} = 5.5 \text{ days}$