Q. The sum of the numerator and denominator of a fraction is 4 more than

twice the numerator. If the numerator and denominator are increased by 3, they are in

the ratio 2 : 3. Determine the fraction.

Let the numerator of fraction be

'x' and denominator be 'y'

As per the first condition

+

–2x + x + y = 4

...........(i)

As per the second condition

Sol.

Fraction

Denominator

Numerator

y

x

=

2x

+ 4

The new Fraction

Denominator

Numerator

y + 3

x + 3

–x + y = 4

y = x + 4

=

∴ 3 (x + 3) = 2 (y + 3)

∴ 3x

∴ 3x – 2y

∴ 3x – 2y = – 3

........(ii)

What is a fraction ?

Fraction is numerator upon denominator

x y

Is means equal to

Keeping like terms together

∴

∴

∴

By cross multiplying we get

+ 3

+ 3

+ 9

= 2y

+ 6

Arrange it in a standard form

Number it as equation (ii)

= 6 – 9

Number it as equation (i)

Since we don’t know the numerator and denominator

What do we need to find ?

Sol.

Substituting (i) in (ii)

=

∴

Or by elimination by substitution method

It is better to use elimination by substitution method

Because we have (i) In the form of

y = something

3x – 2 (x + 4)

= – 3

∴ 3x – 2x – 8

= – 3

∴ 3x – 2x

= – 3 + 8

∴ x

= 5

∴ y

Substituting x = 5 in (i)

= 5 + 4

• y

= 9

Here, we can either solve it by equating the coefficients method