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Explanation
- The sum of the numerator and denominator of a fraction is 11.
- If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3. The fraction can be figure out in this way.
Let suppose y shows numerator and z shows denominator in a fraction.
The sum of numerator and denominator is 11.
y + z = 11 ________ (i)
When 1 is added in y and 2 is taken away from z then
(y + 1)/(z – 2) = 2/3 ________ (ii)
By solving both equations simultaneously, we can easily find out the fraction (y/z = 3/8).
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 = 11 ________ (i)
Multiplying both sides of equation (i) with 2
2y + 2z = 22 ________ (A)
According to second given condition
(y + 1)/(z – 2) = 2/3 ________ (ii)
3(y + 1) = 2(z – 2)
3y + 3 = 2z – 4
3y – 2z = -7 ________ (B)
Adding equation (A) and (B)
2y + 3y + 2z – 2z = 22 – 7
5y = 15
y = 15/5
y = 3
Put y = 3 in equation (i)
3 + z = 11
z = 11 – 3
z = 8
Fraction = 3/8 answer
Conclusion
The sum of the numerator and denominator of a fraction is 11. If 1 is added to the numerator and 2 is subtracted from the denominator, it becomes 2/3. The fraction is 3/8.
