Direct and Inverse Variations | Direct and Inverse Variations Exercise 10.2

Question

55 cows can graze a field in 16 days. How many cows will graze the same field in 10 days?

Solution
Transcript

"hello dear students i am sunita nair from Lido learning i am here to help you solve a problem in in variation which goes like this 55 cows can graze a field in 16 days how many cows will graze the same field in 10 days now let's put in the information that we have in this table next to the picture of the cows grazing in the field so here we have 55 cows can graze a field in 16 days so the question is how many cows will graze the same field in 10 days so let that number of cows which will graze the same field in 10 days be x so we have to find the value of x now we know that if the grass in the field is sufficient for 55 cows for a time of 16 days then if the same field should be sufficient only for 10 days we would need a greater number of cows to graze the field isn't it for the food or for the grass to last only 10 days we would need a greater number of cows so in this case we can see that as a number of cows increase the the time for which they can graze in the same field will reduce so when you have quantities like this which vary inversely if p and q vary inversely that is if as p increases q decreases or if as q increases p decreases then we say that these two quantities are in inverse variation and in such a case the proportionality constant is given by p into q so going back to our problem we know that our p is 16 and our q is 55 so 16 into 55 should be a constant the same constant should be given by the product of 10 into x so x if we solve for x we will get x equal to 16 into 55 divided by 10. so reducing this expression we get the answer is 88 cows 88 cows will graze the same field in 10 days so our answer is 88 i hope you understood the solution to this problem please visit our channel regularly you will find many more homework solutions being explained to you you can subscribe to our channel for updates as well thank you "

Accepted Answer

Let number of cows be ‘x’ cows

We know k = xy

16 × 55 = 10 × x

x = (16×55)/10

= 88

∴ 88 cows can graze the same field in 10 days.

Direct and Inverse Variations | Direct and Inverse Variations Exercise 10.2

Chapters in Mathematics class 8th RD Sharma

Exercises in Direct and Inverse Variations

Question 14