Question

A can do a piece of work in 10 days and B in 12 days. With help of C, they finish the work in 4 days. In how many days C alone can do the same work?

A) 12 B) 15 C) 18 D) 24

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

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$\green{\underline \bold{Given :}}$

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• 'A' can do a piece of work in 10 days.

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• 'B' can do the work in 12 days.

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• With help of 'C', they finish the work in 4 days.

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$\red{\underline \bold{To \: Find:}}$

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• Days in which C alone can do the same work.

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$\large{\orange{\underline{\tt{Solution :-}}}}$

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'A' alone can complete a work in 10 days

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$\underline{\bold{\texttt{A's one day work :}}}$

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$\purple\longrightarrow$ $\sf \dfrac { 1 } { 10 }$

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'B' alone can complete a work in 12 days

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$\underline{\bold{\texttt{B's one day work :}}}$

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$\purple\longrightarrow$ $\sf \dfrac { 1 } { 12 }$

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Let 'x' be the days taken by the 'C' to done the same work

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$\underline{\bold{\texttt{C's one day work :}}}$

$\purple\longrightarrow$ $\sf \dfrac { 1 } { x }$

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'C' along with 'A' and 'B' to complete a work in 4 days

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$\underline{\bold{\texttt{A's + B's + C's one day work : }}}$

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$\purple\longrightarrow$ $\sf \dfrac { 1 } { 4}$

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$\sf \longmapsto A + B + C = \dfrac { 1 } { 4 }$

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$\sf \longmapsto \dfrac { 1 } { 10 } + \dfrac { 1 } { 12 } + \dfrac { 1 } { x } = \dfrac { 1 } { 4 }$

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$\sf \longmapsto \dfrac { 6x + 5x + 60 } { 60x } = \dfrac { 1 } { 4 }$

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$\sf \longmapsto \dfrac { 11x + 60 } { 60x } = \dfrac { 1 } { 4 }$

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$\sf \longmapsto 44x + 240 = 60x$

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$\sf \longmapsto 60x - 44x = 240$

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$\sf \longmapsto 16x = 240$

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$\sf \longmapsto x = \dfrac { 240 } { 16 }$

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$\bf \dashrightarrow x = 15$

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Hence 'C' will take 15 days to do the work alone.

$\rule{200}5$

Answer 2

Answer:

15 days.

Step-by-step explanation:

Time taken by A to do the work = 10 days.

So his one day's work will be 1/10.

Similarly B's one day work will be the reciprocal of the time taken by him.

B's one day's work = 1/12.

Let time taken by C be x.

Therefore, C's one day work = 1/x.

If all of them work together, they complete the work in 4 days.

So together their one day's work will be 1/4.

But their one day's work is given as, 1/10+1/12+1/x

=(6x+5x+60)/60.

Therefore 1/4 = (11x+60)/60x

15x = 11x+60

x = 15 days

Therefore the time taken by C is 15 days.

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