# Linear Equations

## Exercise 2.6 Part 2

##### Solution of NCERT Exercise From Question 5 to 7

Question 5: (7y+4)/(y+2)=-4/3

Solution: Given (7y+4)/(y+2)=-4/3

Multiplying both sides by y+2 we get:

(7y+4)/(y+2)xx(y+2)=-4/3xx(y+2)

Or, 7y+4=(-4y)/(3)-8/3

After transposing -(4y)/(3) to LHS and 4 to RHS we get:

7y+(4y)/(3)=-8/3-4

Or, (21y+4y)/(3)=(-8-12)/(3)

Or, (25y)/(3)=-(20)/(3)

Multiplying both sides by 3 we get:

(25y)/(3)xx3=-(20)/(3)xx3

Or, 25y=-20

After dividing both sides by 25 we get:

(25y)/(25)=-(20)/(25)

Or, y=-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.

Solution: Let the present age of Hari =5x

Present age of Harry =7x

After four years from now:

Age of Hari will be =5x+4

Age of Harry will be =7x+4

As per question, the ratio of their ages after 4 years 3/4

So, (5x+4)/(7x+4)=3/4

After multiplying both sides by 7x+4 we get:

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

Or, 5x+4=(21x)/(4)+3

After transposing (21x)/(4) to LHS and 4 to RHS we get:

5x-(21x)/(4)=3-4

Or, (20x-21x)/(4)=-1

Or, -x/4=-1

Or, x/4=1

After multiplying both sides by 4 we get:

x/4xx4=1xx4

Or, x=4

Since present age of Hari =5x

So, after substituting the value of x, we get:

Present age of Hari =5xx4=20 year

Since present age of Harry =7x

So, after substituting the value of x we get:

Present age of Harry =7xx4=28 year

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 3/2. Find the rational number.

Solution: Let the numerator of the given rational number =x

Since denominator is greater than its numerator by 8

So, denominator =x+8

As per question:

(text(Numerator)+17)/(text(Denominator)-1)=3/2

After substituting the values of numerator and denominator we get:

(x+17)/(x+8-1)=3/2

Or, (x+17)/(x+7)=3/2

After multiplying both sides by x+7 we get:

(x+17)/(x+7)xx(x+7)=3/2xx(x+7)

Or, x+17=(3x)/(2)+(21)/(2)

After transposing (3x)/(2) to LHS and 17 to RHS we get:

x-(3x)/(2)=(21)/(2)-17

Or, (2x-3x)/(2)=(21-34)/(2)

Or, -x/2=-(13)/(2)

After multiplying both sides by 2 we get:

-x/2xx2=-(13)/(2)xx2

Or, -x=-13

Or, x=13

So, demoninator =x+8=13+8=21

So, the rational number =(13)/(21)