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Suptisree Biswas
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Asked: 2024-07-10T23:18:41+05:30 In:

Ram and Shyam together can finish a job in 8 days. Ram can do the same job on his own in 12 days. How long will Shyam take to do the job by himself?

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0%16 days ( 0 voters )
0%20 days ( 0 voters )
100%24 days ( 2 voters )
0%30 days ( 0 voters )
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Ram and Shyam together can finish a job in 8 days. Ram can do the same job on his own in 12 days. How long will Shyam take to do the job by himself?

2 Answers

  1. Suptisree Biswas
    Knowledge Contributor

    Shyam’s 1 day’s work
    = 1/8 – 1/12
    = (3 – 2)/24
    = 1/24
    Therefore, Shyam alone will do the work in 24 days.
    Answer: Shyam alone will do the work in 24 days.

  2. Dhruvi
    Best Answer
    Knowledge Contributor

    Let
    𝑅
    R be the rate at which Ram works (in terms of fraction of job per day).
    Let
    𝑆
    S be the rate at which Shyam works (in terms of fraction of job per day).
    From the problem statement:

    Ram and Shyam together can finish the job in 8 days.
    Ram alone can finish the job in 12 days.
    First, find Ram’s rate
    𝑅
    R:
    𝑅
    =
    1
    12
    R=
    12
    1
    ​

    Next, since Ram and Shyam together can finish the job in 8 days, we have:
    (
    𝑅
    +
    𝑆
    )
    Γ—
    8
    =
    1
    (R+S)Γ—8=1

    Substitute
    𝑅
    =
    1
    12
    R=
    12
    1
    ​
    into the equation:
    (
    1
    12
    +
    𝑆
    )
    Γ—
    8
    =
    1
    (
    12
    1
    ​
    +S)Γ—8=1

    Simplify and solve for
    𝑆
    S:

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