Question : A, B and C can do a piece of work in 30 days, 45 days and 90 days, respectively. A starts the work and he is assisted by B and C together on every third day. In how many days will the work be completed?
Option 1: 23
Option 2: 24
Option 3: 30
Option 4: $22 \frac{1}{2}$
Correct Answer: 23
Solution :
Given :
A can complete work = 30 days
B can complete work = 45 days
C can complete work = 90 days
Total work = LCM of 30, 45 and 90 = 90 units
Efficiency of A $=\frac{90}{30} = 3$ units
Efficiency of B $=\frac{90}{45}=2$ units
Efficiency of C $=\frac{90}{90}=1$ unit
Work done by A, B and C in 3 days = $3A + B + C = 3\times 3\ + 2\ +\ 1\ =\ 12$ units
Work done by A, B and C in 21 days = $12\ \times\ 7\ =\ 84$ units
Remaining Work = 90 – 84 = 6 units
A will complete remaining work = $\frac{6}{3} = 2$ days
Total days = 21 + 2 = 23 days
Hence, the correct answer is 23 days.
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