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Either of the team of A and B or team of C and D can do the a work in

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Senior Manager
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Concentration: Marketing, Strategy
Either of the team of A and B or team of C and D can do the a work in  [#permalink]

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New post 06 Aug 2019, 04:37
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A
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Either of the team of A and B or team of C and D can do the a work in 15 days. Also the same work can be done by the team of A and D in 10 days and by the team of B and C in 30 days. If B alone takes 40 days to complete the work, find the ratio of the number of days taken by the team of B and D and that taken by the team of A and C to complete the work.

1. 1 : 1
2. 3 : 5
3. 3 : 4
4. 1 : 2
5. Cannot be determined
Manager
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New post 06 Aug 2019, 05:59
1
\(\frac{1}{A}\)+\(\frac{1}{B}\)=\(\frac{1}{15}\)

\(\frac{1}{C}\)+\(\frac{1}{D}\)=\(\frac{1}{15}\)

--> \(\frac{1}{A}\)+\(\frac{1}{D}\)=\(\frac{1}{10}\)

--> \(\frac{1}{B}\)+\(\frac{1}{C}\)=\(\frac{1}{30}\)

\(\frac{1}{B}\)=\(\frac{1}{40}\)

--> (\(\frac{1}{B}\)+\(\frac{1}{D}\))=\(\frac{1}{x}\)

--> (\(\frac{1}{A}\)+\(\frac{1}{C}\))=\(\frac{1}{y}\)
-----------------
\(\frac{x}{y}\)=?

\(\frac{1}{C}\)=\(\frac{1}{30}\)-\(\frac{1}{40}\)=\(\frac{1}{120}\)

\(\frac{1}{D}\)=\(\frac{1}{15}\)-\(\frac{1}{120}\)=\(\frac{7}{120}\)

\(\frac{1}{A}\)=\(\frac{1}{15}\)-\(\frac{1}{40}\)=\(\frac{(8-3)}{120}\)=\(\frac{5}{120}\)

\(\frac{1}{B}\)+\(\frac{1}{D}\)=\(\frac{1}{40}\)+\(\frac{7}{120}\)=\(\frac{10}{120}\)=\(\frac{1}{12}\)=\(\frac{1}{x}\) --> x=12

\(\frac{1}{A}\)+\(\frac{1}{C}\)=\(\frac{5}{120}\)+\(\frac{1}{120}\)=\(\frac{6}{120}\)=\(\frac{1}{20}\)=\(\frac{1}{y}\)--> y=20

--> \(\frac{x}{y}\)=\(\frac{12}{20}\)=\(\frac{3}{5}\)

The answer choice is B
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Either of the team of A and B or team of C and D can do the a work in   [#permalink] 06 Aug 2019, 05:59
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