A and B separately do a work in 10 and 15 days respectively. They worked together for some days and then A completed the remaining wor

Question

A and B separately do a work in 10 and 15 days respectively. They worked together
for some days and then A completed the remaining work in 5 days. For how many
days had A and B worked together?

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Ariana 2 weeks 2021-09-07T11:41:34+00:00 1 Answer 0 views 0

Answers ( )

    0
    2021-09-07T11:43:13+00:00

    Answer:

    Answer to this problem is 3 days.

    There are three methods to solve this problem.

    Method-1 Fraction Method

    A completes the work in 10 days -> In 1 day he completes 1/10 part of job.

    B completes the work in 15 days -> In 1 day he completes 1/15 part of job.

    Work done by A & B both in 1 day= 1/10 + 1/15

    =(10+15)/(10×15) = 25/150 = 1/6

    Let both A & B workd for ‘x’ days.

    Work done by them in x day = x/6

    Remaining work = 1-x/6 ………(1)

    This remaining work is done by A alone in 5 days.

    Hence,

    Work done by A in 5 days = Remaining work

    5/10 = 1-x/6 …. From (1)

    x/6 = 1–1/2

    x = 6*1/2

    x=3

    A & B worked for 3 days.

    Method-2 LCM Method

    Let the total units of work be LCM(10,15)=3

    A does 30/10 = 3 units per day work

    B does 30/15 = 2 units per day work

    Together they do (3+2)=5 units of per day work.

    Let say both of them worked for x days.

    Work done by them in x days = 5x

    Remaining work = 30–5x

    This remaining work done by A alone in 5 days

    Hence,

    5*(A’s work per day)= 30–5x

    5*3=30–5x

    x=3

    A & B worked for 3 days.

    Method-3 Percentage Method

    Let the total work be 100%

    A does 100/10 = 10% work in 1 day

    B does 100/15 = 6.66% work in 1 day

    Both A & B do (10+6.66)=16.66% work in 1 day

    Let say they worked for ‘x’ days

    In x days the complete x*16.66% work.

    Remaining work = 100%-x*16.66%

    This remaining work completed by A alone in 5 days

    Work done by A in 5 days = 5*10%= 50%

    Hence,

    Remaining work = work done by A in 5 days

    100 – x*16.66%=50%

    x*16.66% = 100%–50%

    x*16.66% = 50%

    x = 50/16.66

    x=3 days

    A & B worked for 3 days.

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