Question

If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes $\frac{6}{5}$. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes $\frac{2}{5}$. find the fraction.

Answer 1

Given : If the numerator of a fraction is multiplied by 2 and the denominator is reduced by 5 the fraction becomes 6/5. And, if the denominator is doubled and the numerator is increased by 8, the fraction becomes 2/5.  

 

Solution:

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

Then , fraction =   numerator / denominator = x/y

Condition : 1

2x /y - 5 = 6/5

5(2x) = 6(y - 5)

10x = 6y - 30

10x - 6y = - 30  

2(5x - 3y) = - 30

5x - 3y = - 30/2

5x - 3y = - 15………..(1)

Condition : 2

x + 8 /2y  = 2/5

5(x + 8) = 2(2y)

5x + 40 = 4y

5x - 4y = - 40 ………….(2)

On Subtracting equation (2)  from equation (1), we obtain :

5x - 3y = - 15

5x - 4y = - 40  

(-)  (+)     (+)

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y = 25

On Substituting the value of y = 25 in equation (1) we obtain :  

5x - 3y = - 15

5x - 3(25)  = - 15

5x - 75  = - 15

5x  = - 15 + 75

5x = 60

X = 60/5

x = 12

Now , fraction =  x/y = 12/25

Hence, the fraction is 12/25.

Hope this answer will help you…

 

Some more questions from this chapter :  

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?

https://brainly.in/question/17223094

 

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

Answer:

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