Question

10 men or 12 women complete one job in
10 days. In how many days do 5 men and 6
women together complete the job?
1. 8 days
2. 10 days
3. 12 days
4. 15 days
​

Answer 1

10 men + 12 women = 22 people

total days = 10 days

22 people take 10 days to complete the jobs

5 men + 6 women = 11 people

$\frac{10 \times 11 }{22}$

$= \frac{10 \times 11}{22}$

$= \frac{10 \times 1}{2}$

$= 5$

=5 days

Answer 2

2. 10 days is required for 5 men and 6 women together to complete the job.

Given:

No. of men working$=10$

No. of women working$=12$

Total number of days taken by them to complete a work$=10 \ days$

As we know,

$work=Efficiency\times time\ taken$

From the given information, the efficiency of a man=$\frac{1}{10\times10}=\frac{1}{100}$

The efficiency of a woman is=$\frac{1}{10\times 12} =\frac{1}{120}$

Let the time taken by 5 men and 6 women be x days.

So, the efficiency of 5 men $=\frac{5}{100} =\frac{1}{20}$

The efficiency of 6 women $=\frac{6}{120}=\frac{1}{20}$

Hence, the total efficiency of 5 men and 6 women will be $=\frac{1}{20}+ \frac{1}{20}= \frac{1}{10}$

So, using the formula we get,

$x\times\frac{1}{10}=1\\\\ x=10\ days$

Hence the required time will be 10 days.

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