Question : A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days. In how many days will A, B, and C finish it, working all together?
Option 1: $6$ days
Option 2: $5\frac{1}{4}$ days
Option 3: $4\frac{4}{11}$ days
Option 4: $4$ days
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Correct Answer: $4$ days
Solution :
Given:
A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days.
A can do a piece of work in 10 days, B can do it in 12 days and C can do it in 15 days.
So, A in 1 day can do $\frac{1}{10}$ part of the work.
B in 1 day can do $\frac{1}{12}$ part of the work.
and C in 1 day can do $\frac{1}{15}$ part of the work.
Now A, B, and C together in 1 day can do ($\frac{1}{10}$ + $\frac{1}{12}$ + $\frac{1}{15}$) part of the work
= ($\frac{6+5+4}{60}$) = $\frac{15}{60}$ part of the work
Therefore, they together will finish the work in (1 ÷ $\frac{15}{60}$) = $\frac{60}{15}$ = 4 days
Hence, the correct answer is $4$ days.
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