Question : A alone can do $\frac{1}{10}$th part of a work in 8 hours. B alone can do $\frac{1}{5}$th part of the same work in 4 hours. If they work together, then how many hours will they take to complete $\frac{9}{16}$th part of the same work?
Option 1: 9 hours
Option 2: 5 hours
Option 3: 8 hours
Option 4: 4 hours
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Correct Answer: 9 hours
Solution : Let the rate at which A and B can complete the work as $R_a$ and $R_b$, respectively. Given that A can do $\frac{1}{10}$th part of the work in 8 hours. ⇒ $R_a=\frac{1}{10×8}=\frac{1}{80}$ work/hour Given that B can do $\frac{1}{5}$th part of the work in 4 hours. ⇒ $R_b=\frac{1}{5×4}=\frac{1}{20}$ work/hour When A and B work together, their combined rate $R_{ab}$ is the sum of their individual rates: ⇒ $R_{ab}=R_a + R_b=\frac{1}{80}+\frac{1}{20}=\frac{1}{16}$ work/hour. $\therefore$ The time it takes for them to complete $\frac{9}{16}$th part of the work = $\frac{\frac{9}{16}}{\frac{1}{16}}$ = 9 hours Hence, the correct answer is 9 hours.
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Question : A alone can do $\frac{1}{4}$th part of the work in 12 days. B alone can do $\frac{1}{5}$th part of the work in 4 days. In how many days can A and B together can do the same work?
Option 1: $\frac{330}{13}$ days
Option 2: $\frac{240}{17}$ days
Option 3: $\frac{210}{4}$ days
Option 4: $\frac{255}{7}$ days
Question : P, Q, and R alone can complete a piece of work in 30 hours, 10 hours and 15 hours respectively. In how much time will they finish the work if they work together?
Option 1: 5 hours
Option 2: 4 hours
Option 4: 10 hours
Question : Suresh alone can do work in 10 days working 1 hour a day. Balu alone can do the same work in 2 days working 5 hours a day. How many hours do they need to work together in a day to complete the same work in 10 days?
Option 1: 1.5 hours
Option 2: 0.5 hours
Option 3: 1 hour
Option 4: 2 hours
Question : Riya alone can complete a piece of work in 6 days while Siya alone can do the same work in 9 days. If they both work together, then how many days will be required to finish the work?
Option 1: $\frac{45}{13}$
Option 2: $\frac{18}{5}$
Option 3: $\frac{33}{17}$
Option 4: $\frac{55}{16}$
Question : A1, A2, and A3 alone can complete a piece of work in 12 hours, 24 hours, and 16 hours respectively. Working together, in how much time will they complete the same work?
Option 1: 5 hours 30 minutes
Option 2: 5 hours 20 minutes
Option 3: 4 hours 20 minutes
Option 4: 3 hours 30 minutes
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