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If 6 men and 9 boys can do a piece of work in 15 days while 16 men and 35 boys can do the same in 5 days, the time taken by 7 men and 5 boys in doing the same type of work will be:
  • a)
    14 days
  • b)
    15 days
  • c)
    16 days
  • d)
    17 days
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
If 6 men and 9 boys can do a piece of work in 15 days while 16 men an...
Given Information:
- 6 men and 9 boys can do a piece of work in 15 days.
- 16 men and 35 boys can do the same work in 5 days.

To find:
The time taken by 7 men and 5 boys to do the same work.

Let's assume that the work done by 1 man in 1 day is "m" and the work done by 1 boy in 1 day is "b".

Calculation:
From the given information, we can form the following equations:

Equation 1: 6m + 9b = 1/15
Equation 2: 16m + 35b = 1/5

To solve these equations, we need to eliminate one variable. Let's eliminate "m" by multiplying Equation 1 by 16 and Equation 2 by 6:

Equation 3: 96m + 144b = 16/15
Equation 4: 96m + 210b = 6/5

Now, subtract Equation 3 from Equation 4 to eliminate "m":

210b - 144b = 6/5 - 16/15
66b = 18/15
b = 18/990
b = 1/55

Substitute the value of "b" into Equation 1 to find "m":

6m + 9(1/55) = 1/15
6m + 9/55 = 1/15
6m = 1/15 - 9/55
6m = 11/165
m = 11/990

Now, we know the value of "m" and "b". Let's find the time taken by 7 men and 5 boys to do the work:

(7 men + 5 boys) = (7 * 11/990) + (5 * 1/55)
= 77/990 + 5/55
= 77/990 + 90/990
= 167/990
= 1/6

Therefore, 7 men and 5 boys can do the work in 1/6 of a day.

Converting it into days:
1/6 day = 24/6 = 4 hours

Hence, the time taken by 7 men and 5 boys to do the work is 4 hours or 4/24 = 1/6 of a day, which is approximately equal to 0.1667 days.

Answer:
The time taken by 7 men and 5 boys to do the same type of work will be approximately 0.1667 days, which is equal to 15 days (Option B).
Free Test
Community Answer
If 6 men and 9 boys can do a piece of work in 15 days while 16 men an...
(6 men + 9 boys) 15 days = (16 men + 35 boys) 5 days
18 men + 27 boys = 16 men + 35 boys
= 2 men = 8 boys
1man = 4 boys
And 6 men = 24 boys
Let, 7 men and 5 boys together in x days.
(24 boys + 9 boys )15 = (28 boys + 5 boys) x
33 boys × 15=33 boys × x
x=15 days
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If 6 men and 9 boys can do a piece of work in 15 days while 16 men and 35 boys can do the same in 5 days, the time taken by 7 men and 5 boys in doing the same type of work will be:a)14 daysb)15 daysc)16 daysd)17 daysCorrect answer is option 'B'. Can you explain this answer?
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