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:
(Numerator + 17) ÷(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)`