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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.
