| A can do a work in 10 days and B in 20 days. If they together work on it for 5 days, then the fraction of the work that is left, is [SSC (CGL) Pre 2015] |
A) \[\frac{3}{20}\]
B) \[\frac{4}{3}\]
C) \[\frac{1}{4}\]
D) \[\frac{3}{4}\]
Correct Answer: C
Solution :
| Work done by A in one day \[=\frac{1}{10}\] |
| Work done by B in one day \[=\frac{1}{20}\] |
| Total work done by \[(A+B)\] in one day |
| \[=\frac{1}{10}+\frac{1}{20}=\frac{2+1}{20}=\frac{3}{20}\] |
| Work done by \[(A+B)\] in 5 days |
| \[=\frac{3}{20}\times 5=\frac{15}{20}=\frac{3}{4}\] |
| \[\therefore \] Fraction of the work that is left \[=1-\frac{3}{4}=\frac{1}{4}\] |
| Alternate Method |
| Work done in 1 day by A and B |
| \[B=\frac{20+10}{200}=\frac{30}{200}=\frac{3}{20}\] |
| Then, work completed in 5 days \[=\frac{3}{20}\times 5=\frac{3}{4}\] |
| Left work \[=1-\frac{3}{4}=\frac{1}{4}\] |
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