A, B and C can complete a work in 2h. If A does the job alone in 6h and B in 5h, how long will it take for C to finish the job alone ?

Options

A. ` 5 (1)/( 2) h `
B. ` 7 (1)/(2) h `
C. 9 h
D. `4 (1)/( 2) h `

Answer

B

Explanation

Let C alone can finish the job in x h According to the questions,
Work done by A, B and c in 1 h = `(1)/(2)`
`rArr (1)/(6) + (1)/(5) + (1)/(x) = (1)/(2)`
`rArr (1)/(x) = (1)/(2) - (1)/(6) - (1)/(5) = ( 15 - 5 - 6)/( 30)`
`= (4)/(30) = (2)/(15)`
`:. x = 7 (1)/(2) h `