NIFT PG 2019 Question Paper with solutions

Question : 5 of 150

Marks: +1, -0

B

and

C

together can complete a work in 8 days.

A

and

B

together can complete the same work in 12 days and

A

and

C

together can complete the same work in 16 days. In how many days can

A, B

and

C

together complete the same work?

Solution:

According to the question,

(B+C)'{s} 1

day's work

=\;{1}/{8}

...........(i)

(A+B)'

s 1 day's work

=\;{1}/{12}

.......(ii)

(A+C)'{s} 1

day's work

=\;{1}/{16}

.........(iii)
On adding Eqs. (i), (ii) and (iii), we get

2(A+B+C)'{s} 1

day's work

=\;{1}/{8}+\;{1}/{12}+\;{1}/{16}=\;{6+4+3}/{48}=\;{13}/{48}

⇒(A+B+C)'{s} 1

day's work

=\;{13}/{48 × 2}=\;{13}/{96}

∴ A, B and C together can complete the work in

\;{96}/{13}

days

=7 \;{5}/{13}

days

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