| A can do \[\frac{7}{8}\]of work in 28 days, B can do \[\frac{5}{6}\] of the same work in 20 days. The number of days they will take to complete. If they do it together, is [SSG (CPO) 2014] |
A) \[15\frac{3}{7}\,\,\text{days}\]
B) \[17\frac{3}{5}\text{days}\]
C) \[14\frac{5}{7}\,\,\text{days}\]
D) \[13\frac{5}{7}\,\,\text{days}\]
Correct Answer: D
Solution :
| A can do \[\frac{7}{8}\]work in 28 days. |
| \[\therefore \]He alone can do the total work in \[28\times \frac{8}{7}\]days = 32 days. |
| Now, one day work of \[A=\frac{1}{32}\] |
| B can do\[\frac{5}{6}\]work in 20 days |
| He alone can do the total work in \[20\times \frac{6}{5}\]days = 24 days |
| Now, one day work of \[B=\frac{1}{24}\] |
| \[\therefore \]One day work of A and 8 working together |
| \[=\frac{1}{24}+\frac{1}{32}=\frac{4+3}{96}=\frac{7}{96}\] |
| \[\therefore \]Number of days required by A and B working together |
| \[=\frac{96}{7}=13\frac{5}{7}\text{days}\] |
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