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2 men and 5 women can do a piece of work in 4 days, while one man and one woman can finish

it in 12 days. How long would it take for 1 man to do the work?

Answer:

Let’s assume that 1 man takes x days to do work and y days for women.

So, the amount of work done by 1 man in 1 day = 1/x

And the amount of work done by 1 woman in 1 day = 1/y

Now,

The amount of work done by 2 men in 1 day will be = 2/x

And the amount of work done by 5 women in 1 day = 5/y

Then according to the given conditions in the problem, we have

2/x + 5/y = ¼ … (i)

1/x + 1/y = 1/12 … (ii)

Multiplying equation (ii) by 5, we get

5/x + 5/y = 5/12

2/x + 5/y = ¼

(-)—(-)---(-)

3/x = 5/12 – ¼

3/x = (5 - 3)/12

3/x = 2/12 = 1/6

x = 18

Therefore, 1 man can do the work in 18 days.

"hi guys welcome to lido q a video
i am vinit your leader tutor bringing
you this question on your screen
two men and five women can do a piece of
work in four days
while one man and one woman can finish
it in 12 days
how long would it take for one man to do
the work
now we have defined the variables here
the number of days taken by one man be x
and let the number of days taken by one
woman by
then the amount of work done by one man
in one day will be one by x so work done
by two men
in one day will be two by x similarly
work done by one woman
in one day is one by five one by y
work done by five women in one day is
five by y okay
so this should be y
now let us look at the solution
from the first condition
what do we have two men and five men can
do a piece of work in four days
so if they can do the work in four days
amount of work done in one day is
one by four so we can say 2 by
x plus 5 by y is equal to
1 by 4
yeah and from
second condition similarly
we can say that
1 by x plus 1 by y is equal to 1 by 12
this is 2 so multiply
equation 2 by 5 and subtract 1 from it
what do we get so let's do that
multiplying 2 into 5
and subtracting 1 from it we get
5 by x plus 5 by y
minus 2 by x minus 2 by y
is equal to 5 by 12
minus 1 by 4.
so this
this is 5 sorry this cancels out right
so 3 by x is equal to
2 by 12. isn't that right guys
taking the else here okay so this
implies
2x equals to 36 this implies
x is equal to 80
and here we have our answer therefore
number of days
taken by
one man
to do the work is
equal to 18 days isn't that easy guys
if you still have a dog please leave a
comment below do
like the video and subscribe to our
channel i'll see you in our next video
until then bye guys keep practicing"

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