| A, B and C can do a piece of work in 24, 30 and 40 days, respectively. They began the work together but C left 4 days before completion of the work. In how many days was the work done? |
A) 11
B) 12
C) 18
D) 14
Correct Answer: A
Solution :
| Work done by A in one day \[=\frac{1}{24}\] |
| Word done by B in one day \[=\frac{1}{30}\] |
| Work done by C in one day \[=\frac{1}{40}\] |
| Work done by (A + B + C) in 1 day |
| \[=\frac{1}{24}+\frac{1}{30}+\frac{1}{40}=\frac{5+4+3}{120}=\frac{12}{120}\] |
| Work done by (A + B) in 1 day |
| \[=\frac{1}{24}+\frac{1}{30}=\frac{5+4}{120}=\frac{9}{120}\] |
| Work done by (A + B) in last 4 days \[=\frac{9}{120}\times 4=\frac{36}{120}\] |
| \[\therefore \]Work done by (A + B + C)\[=1-\frac{36}{120}=\frac{84}{120}\] |
| Time taken by (A + B + C) to complete the \[\frac{84}{120}\]work |
| \[=\frac{84}{120}\times \frac{120}{12}=7\,\,\text{days}\] |
| \[\therefore \]Total time taken to complete the work |
| \[=7+4=11\,\,\text{days}\] |
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