Question

Please note that this question is from the chapter TIME AND WORK.

​​​​​​Varun and Arun can plough a field in 12 hours and 18 hours respectively. Varun ploughs the field for 4 hours after that he leaves and then Arun ploughs the remaining field. How long did Arun take to plough the remaining field ?

The answer is 12 hours

please try to give the solution correctly and.. mention the formula used

- Regards Mahima

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Answer 1

Let the field be of an area of x sq.units.
*Varun ploughs x units in 12hrs.
so in 1 hour Varun ploughs x/12 sq.units.
*Arun ploughs x squnits in 18 hrs.
So in 1 hour he ploughs x/18 sq.units.

Now given Varun ploughs for 4 hours.and then remaining is done by Arun.
Since for 1 hour Varun ploughs x/12,
for 4 hours he ploughs
4× (x/12). ie
​​​​​ 4×(x/12) = x/3 sq.units is ploughed by Varun.
​​​​​​
Out of a total of X units he ploughed X/3 units.
So remaining field =X-X/3
=2×X/3
This is to be ploughed by Arun.
In 1 hr Arun ploughs X/18 units.
To plough 2×X/3 units,
divide
2×X/3 ÷X/18 = 12 hours

he needs 12 hours.


Miss Mahima here there is no such formula used.its just use of proportion or ratio.
ie 12 hrs : x squnits
1 hr : x/12 squnits
4 hrs : 4 × x/12
ie just multiply 4 on either side of equation on 2nd line. It's just this logic that is used in the question.



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