Question : A and B can do a piece of work in 36 days. B and C can do the same work in 60 days. A and C can do the same work in 45 days. In how many days can B alone complete the same work?
Option 1: 45
Option 2: 60
Option 3: 90
Option 4: 120
Correct Answer: 90
Solution : Let the rates at which A, B, and C can complete the work as $a, b$, and $c$. These rates are the reciprocals of the time it takes each person to complete the work. From the problem, $⇒a + b = \frac{1}{36}$ (A and B can do the work in 36 days) ___(1) $⇒b + c = \frac{1}{60}$ (B and C can do the work in 60 days) ___(2) $⇒a + c = \frac{1}{45}$ (A and C can do the work in 45 days) ___(3) Adding these three equations, $⇒2a + 2b + 2c = \frac{1}{36} + \frac{1}{60} + \frac{1}{45}$ $⇒a + b + c = \frac{1}{30}$ ___(4) From equation (3) and (4), $⇒b = \frac{1}{30} - \frac{1}{45} = \frac{1}{90}$ The time it takes for B to complete the work alone is the reciprocal of B's rate = $\frac{1}{b}$ = 90 days. Hence, the correct answer is 90.
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Question : A and B can do a piece of work in 36 days. B and C can do the same work in 60 days. A and C can do the same work in 45 days. In how many days can A alone complete the same work?
Option 1: 90
Option 3: 120
Option 4: 45
Question : A, B and C together can complete a work in 20 days. A and B together can complete the same work in 30 days. Then, C alone can complete the same work in how many days?
Option 1: 10 days
Option 2: 30 days
Option 3: 45 days
Option 4: 60 days
Question : A can do a certain piece of work in 2.4 times the number of days in which B and C together can do it. If A and B together can do the same piece of work in 27 days and C alone can do it in 75 days, then how many days will B take to do this piece of work alone?
Option 1: 54
Option 2: 48
Option 3: 45
Option 4: 42
Question : Jeevan can do a piece of work alone in 42 days, while Rishi and Jeevan together can do the same piece of work in 27 days. How many days will Rishi take to complete the same piece of work alone?
Option 1: $74 \frac{3}{5}$
Option 2: $75 \frac{1}{5}$
Option 3: $75 \frac{4}{5}$
Option 4: $75 \frac{3}{5}$
Question : John can do a piece of work alone in 20 days, while Ravi can do the same piece of work alone in 28 days. In how many days can the duo complete the same work if they work together?
Option 1: $11 \frac{1}{3}$
Option 2: $12 \frac{2}{3}$
Option 3: $11 \frac{2}{3}$
Option 4: $12 \frac{1}{3}$
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