Question

A can complete a work in 20 days and B
in 30 days. A worked alone for 4 days
and then B completed the remaining
work along with C in 18 days. In how
many days can C working alone complete
the work ?

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Answer 1

Your Answer:

Given:-

• A can complete a work in 20 days and B  in 30 days.
• A worked alone for 4 days  and then B completed the remaining  work along with C in 18 days.

To find:-

• In how  many days can C working alone complete  the work ?

$\tt A \:can\: do\: \dfrac{1}{20}\: of\: a\: piece\: of\: work \: in \:1\: day$

$\tt B \:can\: do\: \dfrac{1}{30}\: of\: a\: piece\: of\: work\: in\: 1\: day$

$\tt Work \: of\: A \: in \: 4 \: days= 4 \times \dfrac{1}{20} = \dfrac{1}{5} \rightarrow\rightarrow\rightarrow\rightarrow\rightarrow (X)$

$\tt Work \: of\: B+C\: in \: 1\: day = \dfrac{1}{18}\rightarrow\rightarrow\rightarrow\rightarrow\rightarrow(Y)$

As from eq (X) After working 4 days by A 4/5 part of work is still remaining. And it is given that 4/5 part of work is done by B and C in remaining 18 days.

So, If B and C wants to complete the work together without taking help of A.

So they need to work $18 \times \dfrac{5}{4} = 22.5\: days$

So,

$\tt \dfrac{1}{30}+\dfrac{1}{a}= \dfrac{1}{22.5}\:\:\:\: (where\:a \: is\:the\:number\:of\:days\:worked\:by\:C) \\\\ \tt \Rightarrow \dfrac{1}{a}=\dfrac{1}{90} \\\\ \tt \Rightarrow a = 90$

So, C can complete work in 90 days