2 men or 3 boys can do a piece of work in 14 days working 6 hours each day. In how many days 6 men and 9 boys will complete a work twice as large working together 2 hours each day?a)12 daysb)14 daysc)16 daysd)15 dayse)10 daysCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

B) 14 days Explanation: 2 m = 3 b So 1m = 3/2 b 6m + 8b = 6 * (3/2) b + 9b = 18 b So we have to find the number of days for 18 boys 3 boys do 1 work in 14 days working 6 hours, let 18 boys do twice work in x days working 2 hrs each day, then B1*D1*H1*W2 = B2*D2*H2*W1
3*14*6*2 = 18*x*2*1 Solve x = 14 days

Answer

B) 14 days Explanation: 2 m = 3 b So 1m = 3/2 b 6m + 8b = 6 * (3/2) b + 9b = 18 b So we have to find the number of days for 18 boys 3 boys do 1 work in 14 days working 6 hours, let 18 boys do twice work in x days working 2 hrs each day, then B1*D1*H1*W2 = B2*D2*H2*W1
3*14*6*2 = 18*x*2*1 Solve x = 14 days

Answer

Given:
2 men or 3 boys can do a piece of work in 14 days working 6 hours each day.

To find:
In how many days 6 men and 9 boys will complete a work twice as large working together 2 hours each day.

Assumptions:
1. The amount of work done by a man and a boy in one hour is the same.
2. The amount of work done by a man and a boy is directly proportional to the number of hours they work.

Solution:
Let's first calculate the total work done by 2 men or 3 boys in 14 days working 6 hours each day.

Work done by 2 men in one day = (2 men) * (6 hours) = 12 man-hours
Work done by 3 boys in one day = (3 boys) * (6 hours) = 18 boy-hours

Work done by 2 men or 3 boys in 14 days = (12 man-hours + 18 boy-hours) * 14 = 420 man-hours or boy-hours

Now, let's calculate the total work required to be done by 6 men and 9 boys working 2 hours each day.

Total work required = 2 * 420 = 840 man-hours or boy-hours

Let's assume the number of days required to complete the work is x.

Work done by 6 men in one day = (6 men) * (2 hours) = 12 man-hours
Work done by 9 boys in one day = (9 boys) * (2 hours) = 18 boy-hours

Work done by 6 men and 9 boys in x days = (12 man-hours + 18 boy-hours) * x = 30x man-hours or boy-hours

Since the work is twice as large, we can equate the two expressions for work done:

30x = 840

Solving for x, we get:

x = 840 / 30 = 28

Therefore, 6 men and 9 boys will complete the work in 28 days working 2 hours each day.

Since we need to find the answer in terms of days, we round up the number of days to the nearest whole number. Thus, the answer is 28 days.

Therefore, the correct answer is option 'B' (14 days).

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