Question

A man, a woman, and a boy individually can complete a certain work in 6, 8, and 24 days respectively. How many boys must assist one man and two women such that the work is completed in 2 days?

Answer 1

Step-by-step explanation:

Given,

A man takes 6 days to complete a certain task.

A woman takes 8 days.

And a boy takes 24 days to complete the work individually..,

Let,

Let, 1 man's one day work be 1/6

Let, 1 man's one day work be 1/61 woman's one day work be 1/8

Let, 1 man's one day work be 1/61 woman's one day work be 1/81 boy's one day work be 1/24

And let the number of boys to assist be x

Now the question conveys that how many boys must assist 1 man and 2 women

So, 2 × 1/8 = 2/8 = 1/4

Now, lets find x ,

1 1 x 1

_ + _ + _ = _ ( 1/2 – 2 days )

6 4 24 2

( LCM of 6, 4 and 24 is 24 )

1 + 1 + x 1

______ = ___

24 2

2 + x 1

____ = ___

24 2

[ Now, lets do cross multiplication ]

( 2 + x ) × 2 [ (2 × 2) + (2 × x) ] = 1 × 24

4 + 2x = 24

2x = 24 - 4

2x = 20

x = 20 ÷ 2

x = 10

So, 10 boys must assist 1 man and 2 women to complete the work in 2 days.

Answer 2

Step-by-step explanation:

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