Question: The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and the work done by a boy in 12 hours. If working 6 hours per day 9 men can complete a work in 6 days, then in how many days can 12 men, 12 women and 12 boys together finish the same work working 8 hours per day??
(A) 1.5
(B) 3
(C) 3 2/3
(D) 4.5
(E) 5
“The work done by a woman in 8 hours is equal to the work done by a man''- is a topic of the GMAT Quantitative reasoning section of the GMAT exam. GMAT quant section enhances the quantitative skills of the students and improves their critical thinking abilities. The students must select the correct option by evaluating the sum with proper mathematical calculations. Basic concepts of mathematics that include knowledge regarding arithmetic, algebra and geometry are necessary to solve GMAT Problem Solving questions. The candidates must have better mathematical skills to crack the calculative problems of the GMAT Quant topic in the problem-solving part. The candidates can practice by answering more questions from the book “501 GMAT Questions”.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and the work done by a boy in 12 hours.
- 9 men can complete a work in 6 days if he works 6 hours per day.
Find Out:
- The number of days 12 men, 12 women and 12 boys together finish the same work working 8 hours per day.
Since work done by a woman in 8 hours = work done by a man in 6 hours = work done by a boy in 12 hours, then we can write:
8w= 6m = 12b
Or, in the next step, we can derive it as, 4w= 3m= 6b
Therefore, it can conclude that 12m + 12w + 12b = 12m + 12 (3/4) m + 12 (3/6) m = 27m
Let, 's the number of days required by 12 men, 12 women and 12 boys together to complete the work working 8 hours per day be x.
Therefore, we get, 27* 8 * x = 9* 6* 6 (since 9 men can finish a work in 6 days by working 6 hours per day)
Therefore, x = 3/2 = 1.5
Hence, 12 men, 12 women and 12 boys together finish the same work working 8 hours per day in 1.5 days
Correct Answer: (A)
Approach Solution 2:
The problem statement suggests that:
Given:
- The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and the work done by a boy in 12 hours.
- 9 men can complete a work in 6 days if he works 6 hours per day.
Find Out:
- The number of days 12 men, 12 women and 12 boys together finish the same work working 8 hours per day.
Let, work done by one woman in 8hours = one man in 6hours = one boy in 12 hours = x
In 1st scenario: 9 men can complete a work in 6 days by working 6 hours per day = 6*9x = 54x
In 2nd scenario: 12 men, 12 women and 12 boys together finish the same work working 8 hours per day
12 men 8 hours = 16 men 6 hours = 16x
12 women 8 hours = 12x
12 boys 8 hours = 8 boys 12 hours = 8x
By summing up, we get, 16x+ 12x + 8x = 36x
If in the first scenario, the task volume “9 men can complete a work in 6 days by working 6 hours per day” = 54x
Then it is required to find the number of days needed to finish the task in the second scenario =36x * n
54x days = 36x * n
n= 54x/36x = 3/2 days = 1.5 days
Hence, 12 men, 12 women and 12 boys together finish the same work working 8 hours per day in 1.5 days
Correct Answer: (A)
Approach Solution 3:
The problem statement implies that:
Given:
- The work done by a woman in 8 hours is equal to the work done by a man in 6 hours and the work done by a boy in 12 hours.
- 9 men can complete a work in 6 days if he works 6 hours per day.
Asked:
To find the number of days 12 men, 12 women and 12 boys together finish the same work working 8 hours per day.
Therefore, the ratio of the time required by a woman, a man and a boy =8:6:12
That can be derived as = 4:3:6
So, 4 women ≡ 3 men ≡ 6 boy
It is asked to find the number of days 12 men, 12 women and 12 boys together finish the same work working 8 hours per day
Therefore, by summing up, we get,
(12 men + 12 women + 12 boys)
=[12+(3/4×12)+(3/6 ×12)] men
= (12+9+6)me
=27 men
Let’s assume the number of days taken is x
The men and days are indirectly proportioned, therefore, we can say, more men= less days
The working hours and the days are indirectly proportioned, therefore, we can say, more working hours= less days
Working hours 8:6
Men 27:9
All of these are proportionate to 6 : x
Therefore, we get, 27 * 8 * x =9 * 6 * 6
Or, x=(9* 6* 6)/(27* 8)
Or, x=3/2 = 1.5
Hence, 12 men, 12 women and 12 boys together finish the same work working 8 hours per day in 1.5 days
Correct Answer: (A)
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