Question

3 men A, B, C Complete the work 10,12,15 respectively if A, B, C Together start the work After 2day A left and next 2 day C also Left Than find how many day the whole work will complete?​

Answer 1

$\huge\sf{\underline{\underline{Question:-}}}$

1. A, B and C can complete a work in 10, 12 and 15 days respectively. They started the work together. But A left the work 5 days before it's completion. B also left the work 2 days after A left. In how many days was the work completed?

$\huge\sf{\underline{\underline{To \: find:-}}}$

• Total number of days to for completing the work

$\huge\sf{\underline{\underline{Let,}}}$

$\sf{A=\dfrac{1}{10},B=\dfrac{1}{12},C=\dfrac{1}{15}}$

$\huge\sf{\underline{\underline{Solution:-}}}$

$\sf{A+B+C=\dfrac{1}{10}+\dfrac{1}{12}+\dfrac{1}{15}} \\ \sf{=\dfrac{6+5+4}{60}=\dfrac{15}{60}=\dfrac{1}{4}}$

So, Therefore C's work 3 days = 3 × 1/15 = 1/5

$\sf{(B+C)'s \: work \: in \: two \: days=2 \times (\dfrac{1}{12}+\dfrac{1}{15})} \\ \sf{=\cancel2 \times \: \dfrac{5+4}{\cancel6\cancel0}=\dfrac{9}{30}=\dfrac{3}{10}}$

$\sf{Remaining \: work \: =1-(\dfrac{1}{5}+\dfrac{3}{10})=\dfrac{10-2-3}{10}} \\ \sf{=\dfrac{1}{2}}$

$\sf{Therefore, \: \dfrac{1}{4} \: work \: done \: by \: A, \: B, \: C \: in \: 1 \: day.}$

⟹ 1/2 = 4 × 1/2 = 2 days

Total time = 2 + 2 + 3 = 7 days

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