Question

P.) Numerator and denominator of a fraction
are in the ratio of 5:6. If 4 is
Subtracted from the numerator, it reduces
to 2/5 And the fraction,​

Answer 1

Solution

Given :-

• Numerator and denominator of a fraction are in the ratio of 5:6
• If 4 is subtracted from the numerator, it reduces to 2/5

Find :-

• These fraction

Explanation

Let,

• Numerator be = x
• Denominator be = y

A/C to question,

(Numerator and denominator of a fraction are in the ratio of 5:6 )

==> x : y = 5:6

==> x/y = 5/6

==>6x - 5y = 0 ----------(1)

Again,

(If 4 is subtracted from the numerator, it reduces to 2/5)

==> (x-4) : y = 2 : 5

==> (x-4)/y = 2/5

==> 5*(x-4) = 2y

==> 5x - 2y = 20 -----------(2)

Multiply by 2 in equ(1) & 5 in equ(2)

• 12x - 10y = 0
• 25x - 10y = 100

___________Sub. it's

==> 12x - 25x = -100

==> -13x = -100

==>x = -100/(-13)

==>x = 100/13

Keep in equ(1)

==> 6 * 100/13 - 5y = 0

==> 5y = 6 * 100/13

==>y = 6*100/(13*5)

==>y = 120/13

Hence

• Fraction be = x/y = (100/13)/(120/13) = 100/120 = 5/6

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Answer Verification

Keep Value of x & y in equ(2)

==> 5 * 100/3 - 2*40 = 20

==> 500/3 - 80 = 20

==> (500-240)/3 = 20

==> 60/3 = 20

==> 20 = 20

L.H.S. = R.H.S.

That's proved

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