2 men and a woman can complete a task in a certain number of days. If 13 men and 12 women work on the same task they can complete it in 1/8thof days required earlier. The number of days taken by 13 men and 12 women is equal to the number of days taken by 4 men and 27 children to finish the same task.If 2 children and a man can complete another task in 12 days. What is the minimum number of days required by 3 women and 1 child to do the same task?Even if they have to work for a fraction of a day, it will be counted as a whole day.a)9 daysb)25 daysc)10 daysd)24 daysCorrect answer is option 'C'. Can you explain this answer?

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2 men and a woman can complete a task in a certain number of days. If 13 men and 12 women work on the same task they can complete it in 1/8^thof days required earlier. The number of days taken by 13 men and 12 women is equal to the number of days taken by 4 men and 27 children to finish the same task.
If 2 children and a man can complete another task in 12 days. What is the minimum number of days required by 3 women and 1 child to do the same task?
Even if they have to work for a fraction of a day, it will be counted as a whole day.

a)
9 days
b)
25 days
c)
10 days
d)
24 days

Correct answer is option 'C'. Can you explain this answer?

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2 men and a woman can complete a task in a certain number of days. If ...

Let the amount of work done by a man in 1 day be "m" units and the amount of work done by a woman in 1 day be "w" units. Let's assume they take N days to complete
As per the first line we can say that
(2m + w) x N = (N/8)(13m + 12w)
On cancelling the common factors and rearranging we get
(2m + w) x 8 = (13 m + 12w)
Which implies 16m + 8w = (13m + 12w)
or 3m = 4w ...(I)
It is also given that it is equal to 4 men and 27 children. Let a child to "c" units of work in a day
Then
(N/8) (13m + 12w) = (N/8)(4m +27c)
Or, 13m + 12w = 4m + 27c
Putting value of w from (I)
13m+9m=4m+27c
or, 18m=27c or 2m = 3c...(II)
Given that another task takes 12 days to be completed by 2 children and a man. Let us assume that it takes x days to be completed by 3 women and 1 child. Equating the amount of work done

Cancelling m and cross multiplying

9.6 days is needed. 10 is the next biggest number .

Answered by Wizius Careers · View profile

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2 men and a woman can complete a task in a certain number of days. If ...

Let's solve the problem step by step:

Step 1: Let's assume that 1 man's work in 1 day is represented by 'x' units, and 1 woman's work in 1 day is represented by 'y' units.

Step 2: According to the given information, 2 men and 1 woman can complete a task in a certain number of days. So, their combined work in 1 day will be:

2x + y units

Step 3: Now, let's consider the second scenario where 13 men and 12 women work on the same task and complete it in 1/8th of the earlier number of days. So, the combined work of these 13 men and 12 women in 1 day will be:

(13x + 12y) * 8 units

Step 4: According to the third scenario, 4 men and 27 children complete the same task in the same number of days as the previous scenario. So, the combined work of these 4 men and 27 children in 1 day will be:

(4x + 27z) units

where 'z' represents the work done by 1 child in 1 day.

Step 5: Now, let's form equations using the given information:

Equation 1: 2x + y = 1 (as 2 men and 1 woman complete the task in 1 day)
Equation 2: (13x + 12y) * 8 = 1 (as 13 men and 12 women complete the task in 1/8th of the earlier number of days)
Equation 3: (4x + 27z) = 1 (as 4 men and 27 children complete the task in the same number of days as the previous scenario)

Step 6: Solve the equations to find the values of 'x', 'y', and 'z'.

From Equation 1, we get: y = 1 - 2x
Substitute this value of 'y' in Equation 2 to get:
(13x + 12(1 - 2x)) * 8 = 1
Simplify and solve the equation to get: x = 1/60

Substitute this value of 'x' in Equation 1 to get:
y = 1 - 2(1/60)
Simplify to get: y = 59/60

Substitute the values of 'x' and 'y' in Equation 3 to get:
4(1/60) + 27z = 1
Solve the equation to get: z = 53/1620

Step 7: Now, let's find the time taken by 3 women and 1 child to complete the task.

The combined work of 3 women and 1 child in 1 day will be:
3y + z = (3 * 59/60) + 53/1620 = 296/300

So, the time taken by 3 women and 1 child to complete the task will be:
1 / (296/300) = 300/296 = 150/148 = 75/74 days

Step 8: Since we need to find the minimum number of days required, we can round up the fraction to the nearest whole number.

Therefore,

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2 men and a woman can complete a task in a certain number of days. If 13 men and 12 women work on the same task they can complete it in 1/8thof days required earlier. The number of days taken by 13 men and 12 women is equal to the number of days taken by 4 men and 27 children to finish the same task.If 2 children and a man can complete another task in 12 days. What is the minimum number of days required by 3 women and 1 child to do the same task?Even if they have to work for a fraction of a day, it will be counted as a whole day.a)9 daysb)25 daysc)10 daysd)24 daysCorrect answer is option 'C'. Can you explain this answer?

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