Check whether the following are in inverse variation or not. x y 13 4 104 0 . 5 8 6 . 5

We know that in inverse variation, the quantities vary inversely, i.e., if one quantity increases, then the other quantity decreases in the same ratio and vice versa. Thus, if two quantities x and y are said to vary in inverse proportion, then the product of x and y remains constant. Now, in the given table, we observe that, when x = 13 and y = 4 , x y = 13 × 4 = 52 . When x = 104 and y = 0 . 5 , then x y = 104 × 0 . 5 = 52 . And, when x = 8 and y = 6 . 5 , then x y = 8 × 6 . 5 = 52 . We observe that the product of x and y are constant in all the cases. Therefore, yes, the given numbers are in inverse proportion.

Check whether the following are in inverse variation or not. x y 1 . 5 5 1 6 0 . 8 7 0 . 6 6

We know that in inverse variation, the quantities vary inversely, i.e., if one quantity increases, then the other quantity decreases in the same ratio and vice versa. Thus, if two quantities x and y are said to vary in inverse proportion, then the product of x and y remains constant. Now, in the given table, we observe that, when x = 1 . 5 and y = 5 , then x y = 1 . 5 × 5 = 7 . 5 . When x = 1 and y = 6 , then x y = 1 × 6 = 6 . When x = 0 . 8 and y = 7 , then x y = 0 . 8 × 7 = 5 . 6 And, when x = 0 . 6 and y = 6 , then x y = 0 . 6 × 6 = 3 . 6 . We observe that the product of x and y are not constant in all the cases. Therefore, no, the given numbers are not in inverse proportion.

Check whether the following are in inverse variation or not. x y 12 4 3 16 2 24 1 . 5 32

We know that in inverse variation, the quantities vary inversely, i.e., if one quantity increases, then the other quantity decreases in the same ratio and vice versa. Thus, if two quantities x and y are said to vary in inverse proportion, then the product of x and y remains constant. Now, in the given table, we observe that, when x = 12 and y = 4 , then x y = 12 × 4 = 48 . When x = 3 and y = 16 , then x y = 3 × 16 = 48 . When x = 2 and y = 24 , then x y = 2 × 24 = 48 And, when x = 1 . 5 and y = 32 , then x y = 1 . 5 × 32 = 48 . We observe that the product of x and y are constant in all the cases. Therefore, yes, the given numbers are in inverse proportion.

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'I Did It' Mathematics>Chapter 14 - Direct and Inverse Variation>Try These!

Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Direct and Inverse Variation, Exercise 4: Try These!

Author:Rupesh Pathak & Vaishali Bhatia

Rupesh Pathak Mathematics Solutions for Exercise - Rupesh Pathak and Vaishali Bhatia Solutions for Chapter: Direct and Inverse Variation, Exercise 4: Try These!

Attempt the practice questions on Chapter 14: Direct and Inverse Variation, Exercise 4: Try These! with hints and solutions to strengthen your understanding. 'I Did It' Mathematics solutions are prepared by Experienced Embibe Experts.