# Problem 1 (Work, Persons, days)

Problem 1 (Work, Men, days): 12 Children take 16 days to complete a work which can be completed by 8 adults in 12 days. 16 adults started working and after 3 days, 10 adults left and 4 children joined them. How many days will it take them to complete the remaining work ?

a) 4              b) 5                  c) 6                     d)

Solution:

To solve this problem we use unitary rule!

i-e

12 children can do the work 16 days

To calculate work done by 1 child we proceed as below;

Let work done by 1 child = ‘x’

we arrange data as under; i-e if number of children increases then days will decrease!

We write this as;

$\frac{1}{12}=\frac {16}{x}$

$==> x=\frac{1}{12\times 16}$

So work done by 1 child is equal to 1/192

in the same way we can calculate;

work done by one adult = 1/96

Since 16 adults worked for 3 days to start 1 work!

so. work done by 16 adults in 3 days ​$$=16\times 3\times \frac{1}{96}$$

Hence remaining work

$=1-\frac{1}{2}=\frac{1}{2}$

Lets see how many days remaining 6 adults and newly joined 4 children will do this 1/2 work !

We proceed as follows;

work of 6 adults and 4 children in 1 day

$=6\times \frac{1}{192}+4\times \frac{1}{92}=\frac{1}{12}$

OR

in other words;

1/12 work is done by 6 adults and 4 children = 1 day

or

1 work is done by 6 adults and 4 children =12 days

or

1/2 work is done by 6 adults and 4 children= 12 x 1/2=6

So, the remaining 1/2 work will be done by 6 adults and 4 children in 6 days!

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