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)`

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