Working alone, three people $P, Q,$ and $R$ can do a certain job in $10, 12,$ and $15$ hours respectively. What

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VJesus12: Legendary Member; Posts: 2276; Joined: Sat Oct 14, 2017 6:10 amFollowed by: 3 members

by VJesus12 » Wed Sep 09, 2020 1:19 am

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Working alone, three people $P, Q,$ and $R$ can do a certain job in $10, 12,$ and $15$ hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least $1$ person must work?

A. $1:3$
B. $1:2$
C. $1:1$
D. $3:1$
E. $15:4$

Answer: E

Source: e-GMAT

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Source: Beat The GMAT — Problem Solving | Wed Sep 09, 2020 1:19 am

swerve: Legendary Member; Posts: 2545; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

Re: Working alone, three people $P, Q,$ and $R$ can do a certain job in $10, 12,$ and $15$ hours respectively. W

by swerve » Wed Sep 09, 2020 6:16 am

VJesus12 wrote: ↑
Wed Sep 09, 2020 1:19 am
Working alone, three people $P, Q,$ and $R$ can do a certain job in $10, 12,$ and $15$ hours respectively. What is the ratio of the maximum and minimum time taken to complete the job, if at every hour, at least $1$ person must work?

A. $1:3$
B. $1:2$
C. $1:1$
D. $3:1$
E. $15:4$

Answer: E

Source: e-GMAT

The time taken will be minimum when all three will work simultaneously $= \dfrac{1}{10} + \dfrac{1}{15} + \dfrac{1}{12} = \dfrac{6+4+5}{60} = \dfrac{15}{60} = \dfrac{1}{4} = 4$ hours

The time taken will be maximum when R will work alone $= 15$ hours

$\dfrac{\text{max}}{\text{min}} = \dfrac{15}{4}$

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