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Question : D1 and D2 can do a piece of work together in 16 days. D2 and D3 can do the same work together in 24 days, while D3 and D1 can do it together in 48 days. In how many days can all 3, working together, do $\frac{5}{6}$ of the work?

Option 1: $\frac{31}{3}$ days

Option 2: $\frac{40}{3}$ days

Option 3: $\frac{35}{3}$ days

Option 4: $\frac{38}{3}$ days


Team Careers360 21st Jan, 2024
Answer (1)
Team Careers360 24th Jan, 2024

Correct Answer: $\frac{40}{3}$ days


Solution : Let $W$ be the total work to be done.
The work done by D 1 + D 2 in one day = $\frac{W}{16}$​
The work done by  D 2 + D 3 in one day = $\frac{W}{24}$
​The work done by D 3 + D 1 in one day = $\frac{W}{48}$​
⇒ 2x [(D 1 + D 2 + D 3 )'s 1 day work] = $\frac{W}{16}$ +$\frac{W}{24}$+$\frac{W}{24}$​
= $\frac{6W}{48}$
⇒ (D 1 + D 2 + D 3 )'s 1 day work = $\frac{W}{16}$
⇒ Time = $\frac{\text{Total Work}}{\text{Combined Rate}}$ = $\frac{\text{$\frac{5W}{6}$}}{\text{$\frac{W}{16}$}}$ = $\frac{5}{6}$ × $\frac{16}{1}$ = $\frac{40}{3}$ days
Hence, the correct answer is $\frac{40}{3}$days.

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