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Explanation
- The difference between the numerator and the denominator of a fraction is 5.
- If 5 is added to its denominator, the fraction is decreased by 5/4.
- The value of the fraction can be figure out in this way.
Let suppose y shows numerator and z shows denominator in a fraction.
The difference between y (numerator) and z (denominator) is 5.
y – z = 5 ________ (i)
The fraction (y/z) decreased by 5/4 when 5 is added to z (denominator).
y/(z +5) = y/z – 5/4 ________ (ii)
By solving both equations simultaneously, we can easily find out the fraction (y/z = 9/4).
To Find
Fraction = ?
Solution
Let suppose
Let suppose y shows numerator and z shows denominator in a fraction.
According to first given condition
y – z = 5 ________ (i)
y = 5 + z ________ (A)
According to second given condition
y/(z +5) = y/z – 5/4 ________ (ii)
y/(z + 5) = (4y – 5z)/4z
4yz = (4y – 5z)(z + 5)
4yz = 4yz + 20y – 5z2 – 25z
5z2 + 25z – 20y = 0
z2 + 5z – 4y = 0 ________ (B)
Put y = z + 5 in equation (B)
z2 + 5z – 4(z + 5) = 0
z2 + 5z – 4z – 20 = 0
z(z + 5) -4(z + 5) = 0
(z + 5)(z – 4) = 0
z + 5 = 0 & z – 4 = 0
z = -5 (not possible) & z = 4 (possible)
Put z = 4 in equation (A)
y = 4 + 5
y = 9
Fraction = 9/4 answer
Conclusion
The difference between the numerator and the denominator of a fraction is 5. If 5 is added to its denominator, the fraction is decreased by 5/4. The fraction is 9/4.