| 24 men can finish a piece of work in 18 days. 30 women can finish the same piece of work in 12 days. In how many days 16 men and 24 women together can finish the same piece of work? [LIC (AO) 2015] |
A) \[8\frac{5}{14}days\]
B) \[10\frac{11}{14}days\]
C) \[9\frac{9}{14}days\]
D) \[9\frac{1}{7}days\]
E) \[8\frac{8}{7}days\]
Correct Answer: C
Solution :
| 24 men can finish a piece of work in 18 days. |
| 1 man can finish in \[=18\times 24\,\,days\] |
| 1 day's work of 24 men \[=\frac{1}{18}\] |
| \[1\,\text{man}\,\,=\frac{1}{18\times 24}\] |
| 1 day's work of 16 men \[=\frac{16}{18\times 24}=\frac{1}{27}\] |
| 1 day's work of 24 women \[=\frac{24}{30\times 12}=\frac{1}{15}\] |
| 1 day's work of 16 men and 24 women |
| \[=\frac{1}{27}+\frac{1}{15}=\frac{15+27}{27\times 15}\] |
| \[=\frac{42}{27\times 15}=\frac{14}{9\times 15}\] |
| Number of days to finish the work by 16 men and women\[=9\frac{9}{14}\,\,\text{days}\] |
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