Rd sharma solutions
Our top 5% students will be awarded a special scholarship to Lido.

Direct and Inverse Variations | Direct and Inverse Variations Exercise 10.2

Question 10

A car can finish a certain journey in 10 hours at the speed of 48 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance?

Looking to do well in your science exam ?  
Learn from an expert tutor. Book a free class!
  • Solution

  • Transcript

Let us consider the speed of the car as ‘x’ km/hr.

We know k = xy

10 × 48 = 8 × x

x = (10×48)/8

= 60

Increased speed = 60 – 48 = 12km/hr.

∴ The speed should be increased by 12 km/hr. to cover the same distance.

"Hello, dear student and Sunita 9 from Lido learning. I'm here to help you solve a sum in inverse variation. It goes like this a car can finish a certain journey in 10 hours at the speed of 48 km/h by how much should it speed be increased so that it may take only eight hours to cover the same distance. So as you can see, I have made a table over here. Let's fill in the values that we have been given. So here we have that a car can finish a certain journey in 10 hours. When the speed is 48 kilometers per hour. Right The question is by how much should it speed be increased so that it may take only 8 hours to cover the same distance. So we shall put eight in the second column. And the new speed by which it can reach its destination in 8 hours Let's denote that by X. Alright now this First Column I have left . To explain the concept of constant the constant in constant of variation in the case of inverse variation now when we look at the speed and time We know that as the speed increases. The time to reach a certain destination will decrease right? So here we have. If the speed is 48 and the destination is reached in 10 hours. To reach the destination in a lesser time that is 8 hours. We will need to increase the speed. So this is a case of inverse variation. So inverse variation is as one. As one quantity P increases and the other quantity Q decreases related quantity Q decreases then P into Q is the constant of proportionality. So in this case, what is our constant of proportionality constant of proportionality is 10 into 48. So since it's a constant 8 into X also should be equal to the same constant. So these two should be equal. Okay, so we have we have this equation here now X is our unknown. So what is x equal to X will be equal to 10 into 48. / it So eat ones I ate it six is a 48. I have 10 into 6, which is 60 kilometers per hour since X is the speed I will. Give it the unit kilometers per hour. Now the question is by how much should it speed be increased? So what was the former speed? The former speed was 48 kilometers per hour. And the new speed is 60 kilometers per hour or the increased speed So By how much you did speed B increase the question is. By how much should the speed be increased? You see this by how much should the speed be increased? So that will be The difference of the new speed and the old So the speed Should be increased. Bye. 60 - 48 Kilometers per hour Which is Twelve So the speech should be increased by 12 kilometers per hour so that the car will reach the same destination in eight hours instead of 10 hours. I hope you understood the solution to this problem. Please visit our Channel regularly, you will find many more such homework solutions being explained to you. Do subscribe to our YouTube channel for updates as well. Thank you."

Set your child up for success with Lido, book a class today!

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta

Question 10

A car can finish a certain journey in 10 hours at the speed of 48 km/hr. By how much should its speed be increased so that it may take only 8 hours to cover the same distance?

  • Solution

  • Transcript

Let us consider the speed of the car as ‘x’ km/hr.

We know k = xy

10 × 48 = 8 × x

x = (10×48)/8

= 60

Increased speed = 60 – 48 = 12km/hr.

∴ The speed should be increased by 12 km/hr. to cover the same distance.

"Hello, dear student and Sunita 9 from Lido learning. I'm here to help you solve a sum in inverse variation. It goes like this a car can finish a certain journey in 10 hours at the speed of 48 km/h by how much should it speed be increased so that it may take only eight hours to cover the same distance. So as you can see, I have made a table over here. Let's fill in the values that we have been given. So here we have that a car can finish a certain journey in 10 hours. When the speed is 48 kilometers per hour. Right The question is by how much should it speed be increased so that it may take only 8 hours to cover the same distance. So we shall put eight in the second column. And the new speed by which it can reach its destination in 8 hours Let's denote that by X. Alright now this First Column I have left . To explain the concept of constant the constant in constant of variation in the case of inverse variation now when we look at the speed and time We know that as the speed increases. The time to reach a certain destination will decrease right? So here we have. If the speed is 48 and the destination is reached in 10 hours. To reach the destination in a lesser time that is 8 hours. We will need to increase the speed. So this is a case of inverse variation. So inverse variation is as one. As one quantity P increases and the other quantity Q decreases related quantity Q decreases then P into Q is the constant of proportionality. So in this case, what is our constant of proportionality constant of proportionality is 10 into 48. So since it's a constant 8 into X also should be equal to the same constant. So these two should be equal. Okay, so we have we have this equation here now X is our unknown. So what is x equal to X will be equal to 10 into 48. / it So eat ones I ate it six is a 48. I have 10 into 6, which is 60 kilometers per hour since X is the speed I will. Give it the unit kilometers per hour. Now the question is by how much should it speed be increased? So what was the former speed? The former speed was 48 kilometers per hour. And the new speed is 60 kilometers per hour or the increased speed So By how much you did speed B increase the question is. By how much should the speed be increased? You see this by how much should the speed be increased? So that will be The difference of the new speed and the old So the speed Should be increased. Bye. 60 - 48 Kilometers per hour Which is Twelve So the speech should be increased by 12 kilometers per hour so that the car will reach the same destination in eight hours instead of 10 hours. I hope you understood the solution to this problem. Please visit our Channel regularly, you will find many more such homework solutions being explained to you. Do subscribe to our YouTube channel for updates as well. Thank you."

Our top 5% students will be awarded a special scholarship to Lido.

subject-cta
Connect with us on social media!
2021 © Quality Tutorials Pvt Ltd All rights reserved
`