Question

If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?

Answer 1

Given : If we add 1 to the numerator and subtract 1 from the denominator, a fraction becomes 1. It also becomes 1/2 if we only add 1 to the denominator. What is the fraction?

 

Solution:

Let the numerator and denominator of the fraction be x and y.  

Then , fraction =   numerator / denominator = x/y

Condition : 1

x + 1/y - 1 = 1

(x + 1) = (y - 1)

x + 1 +  1 = y

x + 2 = y

x - y  = - 2………….(1)  

Condition : 2

x /y +  1 = 1/2

2(x) = 1(y + 1)

2x = y + 1

2x - 1 = y  

y = 2x - 1 ………….(2)

On Substituting the value of y = 2x - 1 in equation (1) we obtain :  

x - y  = - 2

x  - (2x - 1)  = - 2

x  - 2x + 1 = - 2

-x + 1 = - 2

-x  = - 2 - 1

-x = - 3

X = 3

On putting x = 3 in eq (2)  we obtain :

y = 2x - 1

y = 2 (3) - 1

y = 6 - 1

y = 5

Now , fraction =  x/y = 3/5

Hence, the fraction is 3/5.

Hope this answer will help you…

 

Some more questions from this chapter :  

A fraction becomes 9/11 if 2 is added to both numerator and the denominator. If 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction

https://brainly.in/question/17210434

 

A fraction becomes 1/3 if 1 is subtracted from both its numerator and denominator. If 1 is added to both the numerator and denominator, it becomes 1/2. Find the fraction.

https://brainly.in/question/17212180

Answer 2

Let the fraction be = x/y

Equations formed:

• (x + 1)/(y - 1) = 1

=> x + 1 = y - 1

=> x = y - 2

• x/(y + 1) = 1/2

=> 2x = y + 1

Put the previous equation:

=> 2(y - 2) = y + 1

=> 2y - 4 = y + 1

=> y = 5

x = y - 2

=> x = 3

Thus, fraction is 3/5.