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Teams A, B, and C consist of five, eight, and ten members, respectively, such that every member within a team is equally productive. Working separately, teams A, B, and C can complete a certain job in 40 hours, 50 hours, and 4 hours, respectively. Two members from team A, three members from team B, and one member from team C together start the job, and the member from team C leaves after 23 hours. The number of additional member(s) from team B, that would be required to replace the member from team C, to finish the job in the next one hour, is

Solution

✅ Correct Option: 3

Since every member within a team is equally productive, the per-member rate is found by dividing the team's rate by the number of members:

Member of A =140×5=1200= \dfrac{1}{40 \times 5} = \dfrac{1}{200} per hour

Member of B =150×8=1400= \dfrac{1}{50 \times 8} = \dfrac{1}{400} per hour

Member of C =14×10=140= \dfrac{1}{4 \times 10} = \dfrac{1}{40} per hour


Combined rate of 2 members from A, 3 from B, and 1 from C:

=2200+3400+140= \dfrac{2}{200} + \dfrac{3}{400} + \dfrac{1}{40}

=4400+3400+10400= \dfrac{4}{400} + \dfrac{3}{400} + \dfrac{10}{400}

=17400= \dfrac{17}{400} per hour


Work done in 23 hours =23×17400=391400= 23 \times \dfrac{17}{400} = \dfrac{391}{400}

Work remaining =1−391400=9400= 1 - \dfrac{391}{400} = \dfrac{9}{400}


After C leaves, the rate of 2A + 3B:

=2200+3400= \dfrac{2}{200} + \dfrac{3}{400}

=4+3400= \dfrac{4 + 3}{400}

=7400= \dfrac{7}{400} per hour


Let nn = number of additional B members needed. Each B member contributes 1400\dfrac{1}{400} per hour.

To finish 9400\dfrac{9}{400} work in 1 hour:

7400+n400=9400\dfrac{7}{400} + \dfrac{n}{400} = \dfrac{9}{400}

7+n=97 + n = 9

n=2n = 2


The number of additional members from team B required is 22.

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