Question

a man a woman and a boy can complete a work 20 days 30 days and 60 days respectively how amny boys must assist 2 men and 8 women so as to complte the work in 2days

Answer 1

Hello buddy,

Hope this helps you

As a man takes 20 days to complete the work, the work done by him per day is 1/20.
As a woman takes 30 days to complete the work, the work done by her per day is 1/30..
As a boy takes 60 days to complete the work, the work done by it per day is 1/60.

Amount of work done by 2 men and 8 women per day is 2/20  and 8/30 respectively.

2/20 + 8/30 =    6 + 16  =  22/60 
                      -------------
                           60

Thus, in 2 days they will complete 2 x 22/60 = 44/60.

The amount of work left will be

1 - 44/ 60 = 60 - 44     =  16/60
                  ------------
                       60

As the amount of work done by each boy per day 1/60,
the number of boys needed to complete the work is 16 (sixteen) for 2 days.

Answer 2

Hello Dear.

Here is your answer---

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Man's one day work = 1/20 
Amount of work done by 2 men = 2/20
                                                  = 1/10

Woman's one day work = 1/30 
Amount of work done by 8 women = 8/30
                                                       = 4/15

Boy's one day work = 1/60 

Total Work done by Man and Woman in one day = 1/10 + 4/15
                                                                              = (3 + 8)/30
                                                                              = 11/30
                                                                              
Thus, total work done by 2 men and 8 women in one day = 11/30
∴ Total ----------------------------------------------------- 2 days = 22/30
                                                                                        = 11/15

Thus, Remaining Work = $1 - \frac{11}{15}$
                                     = $\frac{15 - 11}{15}$
                                     = 4/15

Number of Boys needed to complete the Remaining Work
=Remaining Work / One day work of Boys.
= $\frac{4/15}{1/60}$
= 4 × 4
= 16 Boys.

Thus, Total of 16 Boys required to complete the Work along with 2 men and 8 women in 2 Days.

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Hope it helps.

Have a Marvelous Day.