Question : A, B, and C can complete a work in 10, 12 and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Number of days required to complete the whole work is:
Option 1: $8\frac{2}{3}$
Option 2: $6\frac{2}{3}$
Option 3: $7$
Option 4: $6$
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Correct Answer: $7$
Solution : Given: A, B, and C can complete a work in 10, 12, and 15 days respectively. A left the work 5 days before the work was completed and B left 2 days after A had left. Let total work = LCM of 10, 12, and 15 = 60 units [Use: Efficiency = $\frac{\text{Total Work}}{\text{Time}}$] So, A's efficiency = $\frac{60}{10}=6$ B's efficiency is = $\frac{60}{12}=5$ C's efficiency is = $\frac{60}{15}=4$ Let $n$ number of days required to complete the 60 units of work. According to the question, $6 \times(n-5) + 5 \times (n-3) + 4 n = 60$ ⇒ $6n-30+5n-15+4n=60$ ⇒ $15n = 105$ ⇒ $n=7$ Hence, the correct answer is $7$.
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Question : P, Q, and R can complete a work alone in 12,15, and 20 days respectively. They started the work together. P left the work 8 days before the work was completed and Q left the work 5 days after P had left. R completed the remaining work alone. How many days will be required to complete the whole work?
Option 1: $\frac{32}{3}$ days
Option 2: $10$ days
Option 3: $\frac{28}{3}$ days
Option 4: $\frac{25}{3}$ days
Question : A and B can do a piece of work in 10 days and 15 days, respectively. They worked together, but 5 days before the completion of the work, A left. In how many days was the work completed?
Option 1: 4
Option 2: 8
Option 3: 6
Option 4: 9
Question : A can finish a work in 25 days, and B can do the same work in 15 days. B worked for 10 days and left the job. A alone can finish the remaining work in how many days?
Option 1: $7 \frac{1}{3}$ days
Option 2: $6 \frac{1}{3}$ days
Option 3: $8 \frac{1}{3}$ days
Option 4: $5 \frac{1}{3}$ days
Question : A and B together can complete a work in 20 days. B and C together can complete the same work in 15 days. If A, B, and C all work together, then the same work gets completed in 10 days. How many days will A and C together take to complete the same work?
Option 1: 8 days
Option 2: 10 days
Option 3: 15 days
Option 4: 12 days
Question : A can do a piece of work in 12 days and B can do the same work in 15 days. If both do the work together, then in how many days will the work be completed?
Option 1: $7 \frac{2}{3}$
Option 2: $6 \frac{2}{3}$
Option 3: $5 \frac{2}{3}$
Option 4: $8 \frac{2}{3}$
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