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Direct and Inverse Variations | Direct and Inverse Variations Exercise 10.2

Question 16

A person has money to buy 25 cycles worth Rs. 500 each. How many cycles he will be able to buy if each cycle is costing Rs. 125 more?

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  • Solution

  • Transcript

Let’s consider number of cycles be ‘x’ cycles Cost of one cycle when increased is = 500 + 125 = 625Rs

We know k = xy

500 × 25 = 625 × x

x = (500×25)/625

= 20

∴ a person can be able to buy 20 cycles if each cycle is costing Rs 125 more.

"Hello, dear student. I'm Sunita Nile from leader learning. I'm here to help you with the problem that goes like this. A person has money to buy 25 Cycles worth rupees 500 each. How many cycles will he be able to buy right? How many cycles will we be able to buy if each cycle is costing you piece 2125 mode? So let's work out the problem the money he has. The money available This Is the cost of 25 Cycles at rupees 500 each, isn't it? Because it says very clearly a person has money to buy 25 Cycles worth rupees 500. So let's calculate the total money. He has it is 25 into 500. Which is equal to these 12,500. Right. Now the question is how many cycles will he be able to buy in each cycle is costing 125 rupees more 125 rupees more than 500. So the cost of the new cycle will be Cost of new cycle Sleeping 500 plus 125 which is equal to rupees 625. Right. So 625 is the cost of the new cycle. And he has rupees 12,500 with him. Right 625 is the cost of the new cycle and he has two beasts 12,500 with him. So how many cycles can be by in that money? It is easy. You just have to divide. 12500 by 625 so number of Cycles he can buy At the new rate Is equal to 12,500? / 625 which works out to let's do it here. People get 20 All right, so he gets 20 Cycles. So, this is our answer. Now if we put these values in this table I will put here. Cost per cycle And here I will put number of Cycles. Right. So cost per cycle in the first case was 500. And the number of Cycles he got at that rate was 25. Now the question here was how many cycles will he be able to buy so I'll put it as X here. Which is our unknown or a question mark right we have to find this out and hear the cost has increased to 500 plus 125, which is 625. So we can see that earlier. We multiplied these two quantities, right 25 into 500. So when we multiply them here also this 525. It is actually what you do in the case of inverse variation. And inverse variation it sure is because if you have two quantities here X and Y as X increases as the cost of the cycle increases we can be sure that we will get the less number of Cycles. For that for the money because the money is fixed for the money available is fixed. What is it money available? It is 500 into 25. Right. So 500 into 25 is actually the constant in the case of inverse variation. So we have 500 in 225, which is a constant of inverse variation. Is also equal to 625 in 2X? Or if we want to find our unknown X is equal to 500. Into 25 divided by 625. So here we will cancel with five or with 2525 ones and 25 goes into 6, 25 25 times and here this cancel with this to give 20. Again, we get that answer is 20. So using the method of variation or using simple logic come to the same answer, which is 20 Cycles. So I hope you found this solution useful to drop a comment in the comment section, and if you need help with more homework problems visit a channel regularly subscribe to it for updates as well. Thank you."

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Question 16

A person has money to buy 25 cycles worth Rs. 500 each. How many cycles he will be able to buy if each cycle is costing Rs. 125 more?

  • Solution

  • Transcript

Let’s consider number of cycles be ‘x’ cycles Cost of one cycle when increased is = 500 + 125 = 625Rs

We know k = xy

500 × 25 = 625 × x

x = (500×25)/625

= 20

∴ a person can be able to buy 20 cycles if each cycle is costing Rs 125 more.

"Hello, dear student. I'm Sunita Nile from leader learning. I'm here to help you with the problem that goes like this. A person has money to buy 25 Cycles worth rupees 500 each. How many cycles will he be able to buy right? How many cycles will we be able to buy if each cycle is costing you piece 2125 mode? So let's work out the problem the money he has. The money available This Is the cost of 25 Cycles at rupees 500 each, isn't it? Because it says very clearly a person has money to buy 25 Cycles worth rupees 500. So let's calculate the total money. He has it is 25 into 500. Which is equal to these 12,500. Right. Now the question is how many cycles will he be able to buy in each cycle is costing 125 rupees more 125 rupees more than 500. So the cost of the new cycle will be Cost of new cycle Sleeping 500 plus 125 which is equal to rupees 625. Right. So 625 is the cost of the new cycle. And he has rupees 12,500 with him. Right 625 is the cost of the new cycle and he has two beasts 12,500 with him. So how many cycles can be by in that money? It is easy. You just have to divide. 12500 by 625 so number of Cycles he can buy At the new rate Is equal to 12,500? / 625 which works out to let's do it here. People get 20 All right, so he gets 20 Cycles. So, this is our answer. Now if we put these values in this table I will put here. Cost per cycle And here I will put number of Cycles. Right. So cost per cycle in the first case was 500. And the number of Cycles he got at that rate was 25. Now the question here was how many cycles will he be able to buy so I'll put it as X here. Which is our unknown or a question mark right we have to find this out and hear the cost has increased to 500 plus 125, which is 625. So we can see that earlier. We multiplied these two quantities, right 25 into 500. So when we multiply them here also this 525. It is actually what you do in the case of inverse variation. And inverse variation it sure is because if you have two quantities here X and Y as X increases as the cost of the cycle increases we can be sure that we will get the less number of Cycles. For that for the money because the money is fixed for the money available is fixed. What is it money available? It is 500 into 25. Right. So 500 into 25 is actually the constant in the case of inverse variation. So we have 500 in 225, which is a constant of inverse variation. Is also equal to 625 in 2X? Or if we want to find our unknown X is equal to 500. Into 25 divided by 625. So here we will cancel with five or with 2525 ones and 25 goes into 6, 25 25 times and here this cancel with this to give 20. Again, we get that answer is 20. So using the method of variation or using simple logic come to the same answer, which is 20 Cycles. So I hope you found this solution useful to drop a comment in the comment section, and if you need help with more homework problems visit a channel regularly subscribe to it for updates as well. Thank you."

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

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