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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Avinash
Where I can find GRE solved questions? – I am asking because I bought a book named as Big Book – but it contains only question without solutions. Any body can help me in this matter?