Question

The numerator of a rational number is less than its denominator by 4. If the numerator is increased by 11 and its denominator is decreased by 1, then the new number becomes 7/3. Find the original number.

Answer 1

Solution -

Let us assume, x is the numerator and y is the denominator of the rational number. 

Therefore, the rational number is = x/y

Given:

x = y - 4 -------------1

Also given:

(x + 11) / (y - 1) = 7/3

3 (x + 11) = 7 (y - 1)

3x + 33 = 7y - 7

7y - 3x =  40  --------------2

Substitute the value of x from equation 1 in equation 2

7y - 3 (y - 4) = 40
7y - 3y + 12 = 40
4y = 40 - 12
4y = 28
y = 7

Therefore, x = y - 4 = 7 - 4 = 3

The original rational number = x/y = 3/7

Answer 2

Let the numerator be x and denominator be
Therefore rational no =x/y
A.T.Q
X+4=y
X-y=-4 - - - - - - - - - - - - 1
X+11/y-1=7/3
7y-1=3x+33
7y-3x=33+1
7y-3x=34 - - - - - - - - - - - - 2
Multiplying 1 by 7 and 2 by 1
7x-7y=-28 - - - - - - - - 3
-3x+7y=34 - - - - - - - - 4
Adding 3 and 4,we will get
4x=62
X=15.5
Substituting X in any Equations to get the value of y
15.5-y=-4
-y = - 4-15.5
-y=-19. 5
Negative sign get cancel
And y=19.5
Therefore rational no is 15.5/19.5