P takes twice as much time as Q or $\frac{3}{2}$ times as much time as R to finish a piece of work. Working together, they can finish the work in 4 hours. Q can do the same work alone in how many hours?

6 hours

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9 hours

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12 hours

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18 hours

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15 hours

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Solution

The correct option is B
9 hours

Suppose P, Q and R take $x, \frac{x}{2}$ and $\frac{2 x}{3}$ hours respectively to finish the work.
Then, $(\frac{1}{x} + \frac{2}{x} + \frac{3}{2 x}) = \frac{1}{4} \Rightarrow \frac{4.5}{x} = \frac{1}{4} \Rightarrow x = 18$
So, Q takes 9 hours to finish the work.

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A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together, they can finish the work in 2 days. B can do the work alone in how many days?

Q. A takes twice as much time as B or thrice as much time as C to finish a piece of work. Working together they can finish the work in 2 days. B can do the work alone in:

A

takes twice as much time as

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or thrice as much time as

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Q. Mark (✓) against the correct answer:
A works twice as fast as B. If both of them can together finish a peice of work in 12 hours, then B alone can do it in
(a) 24 hours
(b) 27 hours
(c) 36 hours
(d) 18 hours

Q. Mark (✓) against the correct answer:
A can finish a piece of work in 12 hours while B can finish it in 15 hours. How long will both take to finish it, working together?
(a) 9 hours
(b)

6 \frac{2}{3}

hours
(c)

6 \frac{3}{4}

hours
(d)

8 \frac{1}{3}

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P takes twice as much time as Q or 32 times as much time as R to finish a piece of work. Working together, they can finish the work in 4 hours. Q can do the same work alone in how many hours?

The correct option is B 9 hours Suppose P, Q and R take x,x2 and 2x3 hours respectively to finish the work. Then, (1x+2x+32x)=14⇒4.5x=14⇒x=18 So, Q takes 9 hours to finish the work.

P takes twice as much time as Q or $\frac{3}{2}$ times as much time as R to finish a piece of work. Working together, they can finish the work in 4 hours. Q can do the same work alone in how many hours?

The correct option is B
9 hours

Suppose P, Q and R take $x, \frac{x}{2}$ and $\frac{2 x}{3}$ hours respectively to finish the work.
Then, $(\frac{1}{x} + \frac{2}{x} + \frac{3}{2 x}) = \frac{1}{4} \Rightarrow \frac{4.5}{x} = \frac{1}{4} \Rightarrow x = 18$
So, Q takes 9 hours to finish the work.