# Exercise 2.6

Question 1 :

Solve : ​$$\dfrac{8x-3}{3x}=2$$

Sol :

​$$\dfrac{8x-3}{3x}=2$$

On multiplying both sides by 3x , we obtain

8x -3 = 6x

8x – 6x = 3

2x = 3

$$x=\dfrac{3}{2}$$

Question 2 :

Solve : ​$$\dfrac{9x}{7-6x}=15$$

Sol :

​$$\dfrac{9x}{7-6x}=15$$

On multiplying both sides by 7 – 6x , we obtain

9x = 15(7 – 6x)

9x = 105 – 90x

9x + 90x = 105

99x = 105

$$x=\dfrac{105}{99}=\dfrac{35}{33}$$

Question 3 :

Solve : ​$$\dfrac{z}{z+15}=\dfrac{4}{9}$$

Sol :

​$$\dfrac{z}{z+15}=\dfrac{4}{9}$$

On multiplying both sides by 9(z + 15) , we obtain

9z = 4(z + 15)

9z = 4z + 60

9z 4z = 60

5z = 60

z = 12

Question 4 :

Solve : ​$$\dfrac{3y+4}{2-6y}=\dfrac{-2}{5}$$

Sol :

​$$\dfrac{3y+4}{2-6y}=\dfrac{-2}{5}$$

On multiplying both sides by 5(2 – 6y) , we obtain

5(3y + 4) = -2(2 – 6y)

15y + 20 = -4 + 12y

15y – 12y = -4 -20

3y = -24

y = – 8

Question 5 :

Solve : ​$$\dfrac{7y+4}{y+2}=-\dfrac{4}{3}$$

Sol :

​$$\dfrac{7y+4}{y+2}=-\dfrac{4}{3}$$

On multiplying both sides by 3(y + 2) , we obtain

3(7y + 4) = – 4(y + 2)

21y +12 = -4y -8

21y + 4y = -8 -12

25y = – 20

$$y=-\dfrac{4}{5}$$

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.

Sol :

Let the common ratio between their ages be x. Therefore, Hari’s age and Haryy’s age will be 5x years and 7x years respectively and four years later, their ages will be (5x + 4) years and (7x + 4) years respectively.

According to the situation given in the question,

$$\dfrac{5x+4}{7x+4}\dfrac{3}{4}$$

4(5x +4) = 3(7x +4)

20x + 16 = 21x + 12

16 – 12 = 21x – 20x

4 = x

Hari’s age ​\begin{align*}&=5x~years\\&=(5\times{4})~years\\&=20~years\end{align*}

Harry’s age ​\begin{align*}&=7x~years\\&=(7\times{4})~years\\&=28~years\end{align*}

Therefore, Hari’s age and Harry’s age are 20 years and 28 years respectively

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 ​$$\dfrac{3}{2}$$​ . Find the rational number.

Sol :

Let the numerator of the rational number be x . Therefore, its denominator will be x + 8

The rational number will be ​$$\dfrac{x}{x+8}$$​ . According to the question,

\begin{align*}&\dfrac{x+17}{x+8-1}=\dfrac{3}{2}\\&\dfrac{x+17}{x+7}=\dfrac{3}{2}\\&2(x+17)=3(x+7)\\&34-21=3x-2x\\&13=x\end{align*}

Numerator of the rational number = x = 13

Denominator of the rational number = x + 18 = 13 + 8 = 21

Rational number ​$$=\dfrac{13}{21}$$