Question

If 30 oxen can plough \[1/{7^{th}}\] of a field in 2 days, how many days 18 oxen will take to do the remaining work?

Answer 1

Hint:
Here we will firstly find the value of the remaining work. Then we will write the work equivalence equation. Then we will solve this equation to get the value of the number of days taken by 18 oxen to do the remaining work.

Complete step by step solution:
The number of oxen is 30 and the number of days of working is 2 days.
Work completed by 30 oxen is \[ = \dfrac{1}{7}\]
Now we will find the remaining work. Therefore, we get
The remaining work is \[ = 1 - \dfrac{1}{7} = \dfrac{{7 - 1}}{7} = \dfrac{6}{7}\]
Let \[x\] be the number of days 18 oxen will take to complete the remaining work.
Now we will find the value of \[x\] by using the work equivalence equation. Therefore, we get
\[ \Rightarrow \dfrac{{30 \times 2}}{{\dfrac{1}{7}}} = \dfrac{{18 \times x}}{{\dfrac{6}{7}}}\]
Now solving the equation to get the value of \[x\], we get
\[ \Rightarrow \dfrac{{18 \times x}}{6} = \dfrac{{60}}{1}\]
\[ \Rightarrow 18 \times x = 60 \times 6 = 360\]
\[ \Rightarrow x = \dfrac{{360}}{{18}} = 20\]

Hence, 18 oxen will take 20 days to do the remaining work.

Note:
Here we have to note that in this question we will use the work equivalence equation which states that the word done by the oxen is equal. We should know that the value of the total work is equal to 1.
Here, it is given to find the days so that we have to first find the remaining work that needs to be completed because in two days only \[1/{7^{th}}\] is done. So, The work equivalence equation is (Quantity of workers \[ \times \] number of days) \[ \div \] work done.
We need to keep in mind that when a great number of manpower (in this question number of oxen) is there, then the work will be done in less time. If man power is less, then the same work will be done in more time.