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    14 men can complete a task in 9 days and 16 women can complete the same task in 7 days. In how many days can 6 men and 8 women complete the task?
    Question

    14 men can complete a task in 9 days and 16 women can complete the same task in 7 days. In how many days can 6 men and 8 women complete the task?

    A.

    7.2

    B.

    8.4

    C.

    9

    D.

    9.6

    Correct option is B

    Given:

    14 men can complete the task in 9 days.

    16 women can complete the task in 7 days.

    We are asked to find how many days 6 men and 8 women can complete the same task.

    Concept Used:

    The rate of work is the reciprocal of the time taken to complete the task.

    Solution:

    Rate of 1 man =114×9=1126 tasks/day \frac{1}{14 \times 9} = \frac{1}{126} \text{ tasks/day}

    Rate of 6 men =6×1126=6126=121 tasks/day 6 \times \frac{1}{126} = \frac{6}{126} = \frac{1}{21} \text{ tasks/day}

    Rate of 1 woman = 116×7=1112 tasks/day\frac{1}{16 \times 7} = \frac{1}{112} \text{ tasks/day}

    Rate of 8 women =8×1112=8112=114 tasks/day 8 \times \frac{1}{112} = \frac{8}{112} = \frac{1}{14} \text{ tasks/day}

    Combined rate of 6 men and 8 women:

    Combined rate =121+114=242+342=542 tasks/day \frac{1}{21} + \frac{1}{14} = \frac{2}{42} + \frac{3}{42} = \frac{5}{42} \text{ tasks/day}

    Time taken to complete 1 task:

    Time taken = 1Combined rate=1542=425=8.4 days\frac{1}{\text{Combined rate}} = \frac{1}{\frac{5}{42}} = \frac{42}{5} = 8.4 \text{ days}

    Thus, 6 men and 8 women can complete the task in 8.4 days.

    Alternate Method: 

    M1D1H1W1=M2D2H2W2\frac{M_1 D_1H_1}{W_1}=\frac{M_2 D_2H_2}{W_2} 

    M = Man, D = Days , H = Hours,   W = Work

    14M ×9=\times 9 =  16W ×7\times 7

    MW=89\frac{M}{W}=\frac 89

    Total Work = 14 ×\times 8 ×\times 9 = 1008

    Now,

    6M + 8W= 6 ×\times 8 + 8 ×\times 9

    = 48 + 72 = 120

    Time taken = 1008120\frac{1008}{120} = 8.4 days​


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