Question

If 5 men take an hour to dig a ditch, how long should it take for 12 men to dig a ditch of the same type?
A.25 mins
B.30mins
C.28 mins
D.20mins

Answer 1

Hint: To solve this problem, we will apply a unitary method. At first, we will find how long it should take to dig a ditch for one man. According to that we will find the required time that twelve men will take to dig the same type of ditch.

Complete step by step answer:
It is given that, \[5\] men take an hour to dig a ditch.
We know that an hour means \[60\] mins.
So, we can write that,
\[5\] men take \[60\] mins to dig a ditch.
Now we will find how long it takes for one man. Surely one man will take more time to dig the ditch.
So, \[1\] man will take \[60 \times 5\] mins to dig a ditch.
Then, for \[12\] men less time will be taken.
So, \[12\] men will take \[\dfrac{{60 \times 5}}{{12}}\]mins to dig a ditch.
On solving the above expression of time we get,
\[\dfrac{{60 \times 5}}{{12}} = \dfrac{{300}}{{12}} = 25\],
\[12\] Men will take \[25\]min to dig the ditch.
Hence, \[25\]minutes of time should be taken for \[12\] men to dig a ditch of the same type.
The correct option is (A) \[25\]min.

Note: This problem can be solved in other way also i.e..,
Since, one man needs more time to complete the work, it implies there is an inverse relation between the man and the time.
So one man requires \[60 \times 5\] minutes
Since 12 men requires less time to complete the work, it implies there is an inverse relation between the man and the time.
So, the required time for \[12\] men will be \[60 \times \dfrac{5}{{12}}\]min \[ = 25\]min