Emdadul28 wrote:
A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left. In how many days C can finish the remaining work?
A. 16
B. 32
C. 64
D. 96
E. None of These
Given: A and B can do a piece of work in 10 days, while B and C can do the same work in 15 days and C and A in 25 days. they started working together, after 4 days A left. After another 4 days B left.
Asked: In how many days C can finish the remaining work?
Let us assume that A, B & C can finish the job in a, b & c days respectively
A and B can do a piece of work in 10 days
\(\frac{1}{a} + \frac{1}{b} = \frac{1}{10}\) (1)
B and C can do the same work in 15 days
\(\frac{1}{b} + \frac{1}{c} = \frac{1}{15}\) (2)
C and A can do the same work in 25 days
\(\frac{1}{c} + \frac{1}{a} = \frac{1}{25}\) (3)
Adding (1) + (2) + (3)
\(2 (\frac{1}{a} + \frac{1}{b}+ \frac{1}{c}) = \frac{1}{10} + \frac{1}{15} + \frac{1}{25} = \frac{31}{150}\)
\frac{1}{a} + \frac{1}{b}+ \frac{1}{c} = \frac{31}{300}[/m] (4)
they started working together, after 4 days A left
In 4 days, work completed = \(4 * \frac{31}{300} = \frac{124}{300}\)
After 4 days, work balance = 1 - \frac{124}{300} = \frac{176}{300} = \frac{44}{75}
Balance work is done by B & C together for 4 days
After another 4 days B left.
Work done by B & C in 4 days\(= 4 * \frac{1}{15} = \frac{4}{15}\)
Work balance = \(\frac{44}{75} - \frac{4}{15} = \frac{24}{75} = \frac{8}{25}\)
Balance work is done by C alone
\(\frac{1}{c} = \frac{31}{300} - \frac{1}{10} = \frac{1}{300}\)
No of days taken by C \(= \frac{8}{25}/\frac{1}{300} = \frac{8*300}{25} = 96\)
IMO D
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