Question : Working alone, A can do the task in 27 hours and B can do it in 54 hours. Find C's share (in Rs.) if A, B, and C get paid Rs. 4,320 for completing a task in 12 hours on which they worked together.
Option 1: 1440
Option 2: 960
Option 3: 1920
Option 4: 1280
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Correct Answer: 1440
Solution : A can do the task in 27 hours and B can do it in 54 hours. With C, together, they complete a task in 12 hours. LCM of 27, 54, and 12 is 108. Let the total work be 108 units. A's working efficiency = $\frac{108}{27}$ = 4 B's working efficiency = $\frac{108}{54}$ = 2 A and B and C's combined working efficiency = $\frac{108}{12}$ = 9 ⇒ C's working efficiency = 9 – 4 – 2 = 3 So, C's share =$\frac{3}{9}×4320$ = Rs. 1440 Hence, the correct answer is 1440.
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Question : A and B can complete a task together in 18 hours. After 6 hours, A leaves. B takes 36 hours to finish the rest of the task. How many hours would it have taken A to do the task if he worked alone?
Option 1: 54
Option 2: 45
Option 3: 21
Option 4: 27
Question : If A had worked alone, it would have taken him 63 hours to complete the task. What is B's share if A and B work together on a task, finishing it in 36 hours, and they get paid Rs. 5,950 for it?
Option 1: Rs. 3,400
Option 2: Rs. 3,600
Option 3: Rs. 2,550
Option 4: Rs. 2,750
Question : B would have taken 10 hours more than what A would have taken to complete a task if each of them worked alone. Working together, they can complete the task in 12 hours. How many hours would B take to do 50% of the task?
Option 1: 30
Option 2: 15
Option 3: 20
Option 4: 10
Question : A and B can do a certain work in 6 hours, and A, B, and C together take 4 hours to do the same. How long will it take for C alone to accomplish the task?
Option 1: 12 hours
Option 2: 4 hours
Option 3: 2 hours
Option 4: 6 hours
Question : Two workers A and B are engaged to do a piece of work. Working alone A would take 8 hours more to complete the work than when working together. If B worked alone, would take $4\frac{1}{2}$ hours more than when working together. The time required to finish the work together is:
Option 1: 5 hours
Option 3: 8 hours
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