Question : Benny can do a piece of work in 24 days. Chethan and David can do the same work individually in 36 and 48 days, respectively. All of them begin the work together. However, Benny leaves the work 4 days before the completion of work and Chethan leaves the work 10 days before the completion of the work. David worked till the end and completed the work. Find the number of days in which the work was completed.
Option 1: 16
Option 2: 20
Option 3: 18
Option 4: 15
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Correct Answer: 16
Solution : The rates of work per day at which Benny, Chethan, and David can complete the work are $\frac{1}{24}$,$\frac{1}{36}$, and $\frac{1}{48}$ respectively. Let the total time taken to complete the work be $T$ days. Benny worked for ($T - 4$) days, Chethan worked for ($T - 10$) days, and David worked for $T$ days. The total work done is equal to 1 (as we're considering the whole work as one unit). According to the question, $\frac{T - 4}{24} + \frac{T - 10}{36} + \frac{T}{48} = 1$ ⇒ $ \frac{6T-24+4T-40+3T}{144} = 1$ ⇒ $\frac{13T}{144} = 1 + \frac{64}{144}$ ⇒ $T=16$ days Hence, the correct answer is 16.
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Question : Aarif, Arun, and Abraham can do work in 12, 20, and 24 days, respectively. They all begin together. Arun leaves the work 3 days and Abraham 4 days before its completion. In how many days is the work finished?
Option 1: 8
Option 2: 10
Option 3: 11
Option 4: 9
Question : A, B and C can work separately in 18, 36 and 54 days. They started the work together, but B and C left 5 days and 10 days, respectively, before the completion of the work. In how many days was the work finished?
Option 1: 15 days
Option 2: 13 days
Option 3: 14 days
Option 4: 12 days
Question : S, T, and U can complete a work in 40, 48, and 60 days, respectively. They received Rs. 10,800 to complete the work. They began the work together, but T left 2 days before the completion of the work and U left 5 days before the completion of the work. S has completed the remaining work alone. What is the share of S (in Rs.) from the total money?
Option 1: 4000
Option 2: 4320
Option 3: 4500
Option 4: 4860
Question : A, B, and C can do work separately in 16, 32, and 48 days, respectively. They started the work together, but B left off eight days and C six days before the completion of the work. In what time is the work finished?
Option 1: 10 days
Option 2: 9 days
Option 3: 12 days
Option 4: 14 days
Question : A, B, and C can do a piece of work in 30 days, 40 days, and 50 days, respectively. Beginning with A, if A, B, and C do the work alternatively then in how many days will the work be finished?
Option 1: $38 \frac{1}{12}$
Option 2: $36 \frac{1}{2}$
Option 3: $36$
Option 4: $39 \frac{1}{12}$
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