Question: A takes 5 more days than B to do a certain job and 9 days more than C; A and B together can do the same job in the same time as C. How many days would A take to do it?
- 10
- 12
- 18
- 16
- 15
“A takes 5 more days than B to do a certain job and 9 days more than C”- is a GMAT Quantitative reasoning topic of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”.
The candidate must possess basic knowledge of mathematical calculations to decipher GMAT Problem-Solving questions. GMAT quant tests and strengthens the mathematical skills of the candidates. The candidate has to act logically to find the right option by mathematical calculations. The calculative mathematical problems in the problem-solving domain of the GMAT Quant topic can be solved with reasonable mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
The problem statement informs that:
Given:
- For certain work, A takes 5 days more than B and 9 days more than C to complete.
- A and B together accomplish the same job in the same time period as C.
Find Out:
- How many days would A require to complete the job individually?
a = b + 5
Then, b = a - 5 (1)
a = c + 9
Then, c = a - 9 (2)
The question states that A and B do the same job at the same time as C
Therefore, it can be said that 1/a + 1/b = 1/c
Putting (1) and (2) in this equation:
1/a + 1/a-5 = 1/a-9
a-5+a/a*(a-5) = 1/a-9
2a-5/a^2- 5a = 1/a-9
2a^2 - 18a - 5a + 45 = a^2 - 5a
2a^2 - 18a + 45 = 0
(a-15) (a-3)
a= 15 or a= 3
Hence, option E is the correct answer.
Approach Solution 2:
According to the problem statement, A and B complete the job at the same time as C. To do the work individually A needs 5 days more than B and 9 days more than C. Find out the days A needed to do the job.
Let the entire work is 1 unit.
Let B needed time to do the job be b days. Then, the time required by A will be b + 5 days
Let C needed time to do the job be c days. Then, the time required by A will be c + 9 days
Therefore, it can be said that b + 5 = c + 9
Or, c = b - 4.
A and B can together complete the job at the same time as C. Therefore, the sum of A and B is equal to C.
1/a + 1/b = 1/c
Substituting the value of a and c:
1/b+5 + 1/b = 1/ (b - 4)
Doing the LCM on the left-hand side and simplifying, it can be stated that
b+b+5/ b (b+5) = 1/ (b-4)
By cross-multiplying and simplifying, it can get,
2b^2 - 3b - 20 = b^2 + 5b
By simplifying further, it can be stated that
b^2 - 8b -20 = 0
(b-10) (b+2) = 0
Therefore, b= 10 since b= -2 is a negative integer and is not a correct proposition.
If b= 10, then a = b+5 = 15
Thus, A would require 15 days to do the job.
Hence, option E is the correct answer.
Approach Solution 3:
The problem statement says that A takes 9 days more than C and 5 days more than B to complete a job. Together A and B take the same time as C. How many days does A alone require to complete the job?
Let the day required by C alone be n
Therefore, in one day, work accomplished by C= 1/n part
Time required by A to complete the same work = n + 9 days
Therefore, in one day, work accomplished by A = 1/n+9
A and B together takes time to do the job as C
Therefore, in one day, work accomplished by A and B together= work done by C in one day = 1/n
Let work accomplished by B in one day be b
Therefore, 1/n = b + (1/n+9)
That is, b= 9/n(n+9)
Thus, B takes n(n+9)/9 days to complete the work alone.
As per the question suggested, time taken by A alone = time taken by B alone + 5
Therefore, it can be implied that n + 9= n(n + 9)/9 + 5
By simplifying it, it can be concluded that n^2 = 36 and n= 6 days
Thus A alone can complete the job in n+9 = 6 + 9 = 15 days
Hence, option E is the correct answer.
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