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

[VJesus12]

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

[swerve]

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

\(\dfrac{\text{max}}{\text{min}} = \dfrac{15}{4}\)