A) \[56\frac{2}{3}\]days
B) \[53\frac{1}{3}\]days
C) 52 days
D) 50 days
Correct Answer: A
Solution :
| For the first 10 days 40 men worked. |
| \[\therefore \] 40 men can complete the work in 40 days |
| \[\therefore \] 1 man will complete the same work in 1600 days |
| \[\therefore \] 1 man's 1 day's work \[=\frac{1}{1600}\] |
| \[\therefore \] Part of work done in first 10 days \[=\frac{1}{4}\] |
| For the next 10 days 35 men worked. |
| Part of the work done \[=\frac{1\times 35\times 10}{1600}=\frac{7}{32}\]Parts |
| For the next 10 days, 30 men worked |
| Part of the work done \[=\frac{30\times 10}{1600}=\frac{3}{16}\] |
| For the next 10 days, 25 men worked. |
| Part of the work done \[=\frac{25\times 10}{1600}=\frac{5}{32}\] |
| Similarly, part of the work done by 20 men in next 10 days \[=\frac{20\times 10}{1600}=\frac{1}{8}\] |
| Work done to 50 days |
| \[=\frac{1}{4}+\frac{7}{32}+\frac{3}{16}+\frac{5}{32}+\frac{1}{8}\] |
| \[=\frac{8+7+6+5+4}{32}=\frac{30}{32}=\frac{15}{16}\] |
| \[\therefore \] Remaining work \[=1-\frac{15}{16}=\frac{1}{16}\] |
| Now 15 men remain to work 15 men's 1 day's work \[=\frac{15}{1600}\] |
| \[\therefore \] Time taken to complete \[\frac{1}{16}\]part of work |
| \[=\frac{1600}{15}\times \frac{1}{16}=\frac{20}{3}=6\frac{2}{3}\text{days}\] |
| \[\therefore \] Total time \[=50+6\frac{2}{3}=56\frac{2}{3}\text{days}\] |
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