Question: A and B can finish a work in 10 days when working together. B and C working together can finish the same work in 12 days and A and C working together can finish the work in 15 days. In how many days will the work get over if all three A, B and C work together?
- 5
- 6
- 8
- 4
- 3
Correct Answer: C
Solution and Explanation
Approach Solution 1:
Given:
- A and B can finish a work in 10 days when working together.
- B and C working together can finish the same work in 12 days
- A and C working together can finish the work in 15 days
Find out:
- In how many days will the work get over if all three A, B and C work together
We will consider the LCM of 10, 12 and 15
The LCM is 60.
Hence, let us consider that the total work be 60 Units.
Thus, we have -
Efficiency of A + B = 6 (60/10)
Efficiency of B + C = 5 (60/12)
Efficiency of A + C = 4 (60/15)
Combined efficiency of A+B+C= 6+5+4/2 = 15/2
Thus, Time required by A , B and C to complete the work is
60∗ 2/15 = 8
Approach Solution 2:
Given:
- A and B can finish a work in 10 days when working together.
- B and C working together can finish the same work in 12 days
- A and C working together can finish the work in 15 days
Find out:
- In how many days will the work get over if all three A, B and C work together
We can create the equations:
1/A + 1/B = 1/10
1/B + 1/C = 1/12
1/A + 1/C = 1/15
Adding the equations together, we have:
2/A + 2/B + 2/C = 1/10 + 1/12 + 1/15
2/A + 2/B + 2/C = 6/60 + 5/60 + 4/60
2/A + 2/B + 2/C = 15/60
2/A + 2/B + 2/C = 1/4
To determine 1/A + 1/B + 1/C, we multiply the above equation by ½, and we have:
1/A + 1/B + 1/C = 1/8
Therefore, the job can be completed in 1/(1/8) = 8 days if all 3 people work together.
Approach Solution 3:
We can create the equations:
1/A + 1/B = 1/10
1/B + 1/C = 1/12
1/A + 1/C = 1/15
Adding the equations together, we have:
2/A + 2/B + 2/C = 1/10 + 1/12 + 1/15
2/A + 2/B + 2/C = 6/60 + 5/60 + 4/60
2/A + 2/B + 2/C = 15/60
2/A + 2/B + 2/C = 1/4
To determine 1/A + 1/B + 1/C, we multiply the above equation by ½, and we have:
1/A + 1/B + 1/C = 1/8
Therefore, the job can be completed in 1/(1/8) = 8 days if all 3 people work together.
“A and B can finish a work in 10 days when working together. B and C”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.
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