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The Denominator of a Fraction is 3 more than the Numerator. If the Numerator as well as the Denominator is Increased by 4, the Fraction Becomes 4/5. What was the Original Fraction?

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Explanation

  • The denominator of a fraction is 3 more than the numerator.
  • If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5.
  • The original fraction can be figure out in this way.

Let suppose y shows numerator and z shows denominator in a fraction.

z (denominator) is 3 more than y (numerator).

z = y + 3 ________ (i)

The fraction becomes 4/5 when numerator and denominator is increased by 4.

(y + 4)/(z + 4) = 4/5 ________ (ii)

By solving both equations simultaneously, we can easily find out the fraction (y/z = 8/11).

To Find

Fraction = ?

Solution

Let suppose

Let suppose y shows numerator and z shows denominator in a fraction.

According to first given condition

z = y + 3 ________ (i)

y – z = -3

Multiplying both sides of equation (i) with -4

-4y + 4z = 12 ________ (A)

According to second given condition

(y + 4)/(z + 4) = 4/5 ________ (ii)

5(y + 4) = 4(z + 4)

5y + 20 = 4z + 16

5y – 4z = 16 – 20

5y – 4z = -4 ________ (B)

Adding equation (A) and (B)

-4y + 5y + 4z – 4z = 12 – 4

y = 8

Put y = 8 in equation (i)

z = 8 + 3

z = 11

Fraction = 8/11 answer

Conclusion

The denominator of a fraction is 3 more than the numerator. If the numerator as well as the denominator is increased by 4, the fraction becomes 4/5. The original fraction is 8/11.

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