Haryana State Board HBSE 8th Class Maths Solutions Chapter 13 Direct and Inverse Proportions InText Questions and Answers.

## Haryana Board 8th Class Maths Solutions Chapter 13 Direct and Inverse Proportions InText Questions

Try These (Page 204)

Question 1.

Observe the following tables and find if x and y are directly proportional.

Solution:

\(\frac{x}{y}\) = \(\frac{x_{1}}{y_{1}}\) = \(\frac{x_{2}}{y_{2}}\) ………..

Question 2.

Principal = Rs. 1000, Rate = 8% per annum. Fill in the following table and find which type of interest (simple or compound) changes in direct proportion with time period.

Solution:

Try These (Page 211)

Question 3.

Observe the following tables and find which pair of variables (here x and y) are in inverse proportion.

Solution:

(i) Two quantities are said to vary inversely if the increase in one quantity causes the decrease in the other quantity.

In this case if y_{1}, y_{2} are the values of y corresponding to the values x_{1}, x_{2} of x respectively then

x_{1}y_{1} = x_{2}y_{2}

\(\frac{x_{1}}{x_{2}}\) = \(\frac{y_{1}}{y_{2}}\)

x × y = x_{1}y_{1} = x_{2}y_{2} = ………

x × y ≠ 50 × 5 ≠ 40 × 6 ≠ 30 × 7 ≠ 20 × 8

Hence, table (i) is not inversely proportional.

(ii) x × y = x_{1} × y_{1} = x_{2} × y_{2}

= x_{3} × y_{3}…………

= 100 × 60 = 200 × 30

= 300 × 20 = 400 × 15

= 600 = 6000 = 6000 = 6000

Hence table (ii) is inversely proportional.

(iii) x × y = x_{1}y_{1}= x_{2} × y_{2} = x_{3} × y_{3} = ……..

= 90 × 10 = 60 × 15

= 45 × 20 = 30 × 25

= 20 × 30 = 5 × 35

= 900 = 900 = 900 ≠ 750

≠ 600 ≠ 175

Hence, in table (iii) 90, 10; 60, 15; 45, 20 are inversely proportion but other are not inversely proportional.