If $A$ can do a piece of work in $4$ hours, $B$ and $C$ together in $3$ hours and $A$ and $C$ together in $2$ hours. How long will $B$ alone take to do it?

10

hours

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12

hours

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8

hours

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24

hours

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Solution

The correct option is C $12$ hours
$A$ 's 1 hour's work $= \frac{1}{4}$
$(B + C)$ 's 1 hour's work $= \frac{1}{3}$
$(A + C)$ 's 1 hour's work $= \frac{1}{2}$
$∴ C$ 's 1 hour's work $= \frac{1}{2} - \frac{1}{4} = \frac{1}{4}$
$B$ 's 1 hour's work $= \frac{1}{3} - \frac{1}{4} = \frac{1}{12}$
Hence, $B$ will complete the whole work in 12 days.

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If A can do a piece of work in 4 hours, B and C together in 3 hours and A and C together in 2 hours. How long will B alone take to do it?

The correct option is C 12 hoursA's 1 hour's work =14(B+C)'s 1 hour's work =13(A+C)'s 1 hour's work =12∴C's 1 hour's work =12−14=14B's 1 hour's work =13−14=112Hence, B will complete the whole work in 12 days.

If $A$ can do a piece of work in $4$ hours, $B$ and $C$ together in $3$ hours and $A$ and $C$ together in $2$ hours. How long will $B$ alone take to do it?