| Two workers A and B working together complete the job in 5 days. If A worked twice as efficiently as he actually did and B worked 1/3 as efficiently as he actually did, the work would have been completed in 3 days. To complete the job alone, A would require [SSC (CGL) 2013] |
A) \[5\frac{1}{2}\text{days}\]
B) \[6\frac{1}{4}\text{days}\]
C) (c)\[7\frac{1}{2}\text{days}\]
D) \[8\frac{3}{4}\text{days}\]
Correct Answer: B
Solution :
| Let A and B complete the job in x and y days, respectively. |
| Then, \[\frac{1}{x}+\frac{1}{y}=\frac{1}{5}\] (i) |
| After changing efficiencies, A would be able to completed the work in \[\frac{x}{2}\]days and B in 3y days. |
| \[\therefore \] \[\frac{2}{x}+\frac{1}{3y}=\frac{1}{3}\] (ii) |
| Solving Eqs. (i) and (ii), we get \[x=\frac{25}{4}=6\frac{1}{4}\text{days}\] |
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