# RD Sharma Solutions Class 8 Mathematics Solutions for Direct and Inverse Variations Exercise 10.2 in Chapter 10 - Direct and Inverse Variations

Question 8 Direct and Inverse Variations Exercise 10.2

1200 men can finish a stock of food in 35 days. How many more men should join them so that the same stock may last for 25 days?

Let the number of men joined be ‘x’ men

Total men = 1200

We know k = xy

1200 × 35 = x × 25

x = (1200×35)/25

= 1680

So, 1680 – 1200 = 480 Men

∴ 480 men should join for the same stock to last for 25 days.

Video transcript
"Hello dear student. I'm Sunita mile from grito learning. I am here to help you with a homework problem that goes like this. 1200 men can finish a stock of food in 35 days how many more men should join them so that the same Stock May last for 25 days. So let's put in the information given in this table that I have drawn below. So here you have the number of men. Is 1200. Who can finish a stock of food in 35 days? The question is how many more men should join them so that the same Stock May last for 25 days? Alright, so this is our unknown the number of men. Who can have the food for 25 days? So let's indicate that by a letter x. Okay. Now we know that these two quantities the number of men in the time in time in days. Vary inversely that is if the number of men are increased then the food will last for a short of time. Then 35 days. So we can assume that X the number of men who can eat the food for 25 days will be more than 1,200. So we see that as the number of men go up. The num time in days goes down. So this is a case of inverse variation. We're in general. If one quantity P if a quantity p goes up. Thank you goes down. Okay, so if p goes if p is increased. Then Q is reduced. Alright, so this is a case of inverse variation. So in such a case. There is a constant of proportionality given by P into Q. P into Q is our constant So let's work out the value of our constant p in this case is 1200. Q is 35 so P into Q is 1200 into 35 is equal to the same constant is given by the values X multiplied by 25. Because the constant is the same for all the pairs of p and Q. So let's find out what our X. So now we have an expression where we can get the value of x so X is equal to 1200 into 35 upon 25. So let's reduce this fraction. And once more So we have a value of x which is equal to 240 x 7. So let's do the working here. We get 1680 so our X we found is 1680. So let's substitute that value of x. Right. Now the question is how many more men should join the existing 1200 so that the same stock can last for 25 days? So the number of And who should join the 1200 men is given by 1618 - 1200 which is equal to 480. Therefore 480 men Shoot Join So, this is how we have solved the problem. I hope this video helped you to understand the solution. Please visit our Channel regularly, you will find many more homework solutions being explained to you to subscribe to our YouTube channel for updates as well. Thank you."
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