Question

A takes 40 minutes to do a job. B takes 1 hour to do the same job.A,B and C start doing that job together. They complete it in only 15 minutes. Had C been alone,how much time would he have taken to do that job

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{A takes 40 minutes to do a job.B takes 1 hour to do the same job.}$

$\textsf{A,B and c together complete the work 15 minutes}$

$\underline{\textsf{To find:}}$

$\textsf{How much time would be have taken by C alone}$

$\underline{\textsf{Solution:}}$

$\textsf{From the given information,}$

$\textsf{A's 1 minute work}\,\mathsf{=\dfrac{1}{40}}$

$\textsf{B's 1 minute work}\,\mathsf{=\dfrac{1}{60}}$

$\textsf{Let C's 1 minute work be}\;\mathsf{\dfrac{1}{x}}$..........(1)

$\textsf{(A+B+C)'s 1 minute work}\,\mathsf{=\dfrac{1}{40}+\dfrac{1}{60}+\dfrac{1}{x}}}$

$\textsf{Since they together the work in 15 minutes,}$

$\textsf{(A+B+C)'s 1 minute work}\;\mathsf{=\dfrac{1}{15}}$.........(2)

$\textsf{From (1) and (2), we get}$

$\mathsf{\dfrac{1}{40}+\dfrac{1}{60}+\dfrac{1}{x}=\dfrac{1}{15}}$

$\mathsf{\dfrac{3x+2x+120}{120x}=\dfrac{1}{15}}$

$\mathsf{\dfrac{5x+120}{120x}=\dfrac{1}{15}}$

$\mathsf{\dfrac{5x+120}{8x}=1}$

$\mathsf{5x+120=8x}$

$\mathsf{120=8x-5x}$

$\mathsf{120=3x}$

$\implies\mathsf{x=40}$

$\underline{\textsf{Answer:}}$

$\textsf{C alone can complete the work in 40 minutes}$

Answer 2

Answer:

Step-by-step explanation: