Question

IX.
The denominator of a fraction is 4 more than twice its
numerator. Denominator becomes 12 times the numerator,
if both the numerator and the denominator are reduced by
6. Find the fraction.
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Answer 1

✬ Fraction = 7/18 ✬

Explanation:

Given:

• Denominator of fraction is 4 more than twice its numerator.
• After reducing both numerator & denominator by 6 denominator become 12 times of numerator.

To Find:

• What is the fraction ?

Solution: Let the numerator be x and denominator be y. Therefore

➟ Fraction = x/y = numerator/denominator

Also it is given that

➟ Denominator = 4 more than 2x

➟ y = 4 + 2x...........i

[ Reducing 7 from both ]

• Numerator = (x – 6)
• Denominator = (y – 6)

A/q

• After reducing both numerator & denominator by 6 denominator become 12 times of numerator.

$\implies{\rm }$ 12(x – 6) = (y – 6)

$\implies{\rm }$ 12x – 72 = y – 6

$\implies{\rm }$ 12x – y = – 6 + 72

$\implies{\rm }$ 12x – y = 66

$\implies{\rm }$ 12x – (4 + 2x) = 66

$\implies{\rm }$ 12x – 4 – 2x = 66

$\implies{\rm }$ 10x = 66 + 4

$\implies{\rm }$ x = 70/10 = 7

So numerator of fraction is 7.

• Denominator = 4 + 2(7) = 18

Hence, required fraction is x/y = 7/18

Answer 2

Fraction = 7/18

Given:

• Denominator of fraction is 4 more than twice is numerator .
• After reducing both numerator and denominator become 12 times of numerator.

To find: What is fraction?

Solution: Let the numerator be x and denominator be y.

Therefore

Fraction =x/y= numerator /denominator

Also it is given that:

Denominator = 4 more than 2x

y = 4 + 2x

( Reducing 7 from both)

• Numerator =(x-6)
• Denominator =(y-6)

A/q

• After reducing both numerator and denominator by 6 denominator becomes 12 times of numerator

12(x-6)= ( y-6)

12x - 72 = y-6

12x- y = -6+72

12x-y = 66

12x - ( 4x+ 2x) = 66

12x - 4 - 2x = 66

10x = 66+4

x = 70/10 = 7

So numerator of fraction is 7.

Denominator = 4 + 2(7) = 18

Hence, Required fraction is x/y = 7/18.

Hope it helps you.