## MP Board Class 8th Maths Solutions Chapter 2 Linear Equations in One Variable Ex 2.6

Solve the following equations.

Question 1.

\(\frac{8 x-3}{3 x}=2\)

Solution:

We have, \(\frac{8 x-3}{3 x}\) = 2

⇒ 8x – 3 = 2 × 3

⇒ 8x – 3 = 6x ⇒ 8x – 6x = 3 ⇒ 2x = 3

⇒ x = \(\frac{3}{2}\), which is the required solution.

Question 2.

\(\frac{9 x}{7-6 x}=15\)

Solution:

Question 3.

\(\frac{z}{z+15}=\frac{4}{9}\)

Solution:

Question 4.

\(\frac{3 y+4}{2-6 y}=\frac{-2}{5}\)

Solution:

Question 5.

\(\frac{7 y+4}{y+2}=\frac{-4}{3}\)

Solution:

Question 6.

The ages of Hari and Harry are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. Find their present ages.

Solution:

Let the present ages of Hari and Harry be 5x and 7x respectively.

After 4 years, Hari’s age = (5x + 4) years and Harry’s age = (7x + 4) years

∴ Hari’s present age = 5x = 5 × 4 = 20 years and Harry’s present age = 7x = 7 × 4 = 28 years

Question 7.

The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number

obtained is \(\frac{3}{2}\). Find the rational number.

Solution:

Let the numerator of the rational number be x.

∴ The denominator is x + 8.

According to question, we have

New numerator = x + 17 and

New denominator = (x + 8) – 1 = x + 7

⇒ 2(x + 17) = 3(x + 7) ⇒ 2x + 34 = 3x + 21

⇒ 34 – 21 = 3x – 2x ⇒ 13 = x

Thus, numerator = x = 13

and denominator = x + 8 = 13 + 8 = 21

Hence, the rational number is \(\frac{13}{21}\).