Question

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes $\frac{1}{4}$. And when 6 is added to numerator and the denominator is multiplied by 3, it becomes $\frac{2}{3}$. Find the fraction.

Answer 1

Given : When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4. And, when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3.  

Solution:

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

Then , fraction =   numerator / denominator = x/y

Condition : 1

x - 2 /y + 3 = 1/4

4(x - 2) =  y + 3  

4x - 8 = y + 3

4x - y = 3 + 8

4x - y = 11 ………..(1)

Condition : 2

x + 6 /3y  = 2/3

3(x + 6) = 2(3y)

3x + 18 = 6y

3x - 6y = - 18 ………….(2)

On multiplying equation (1) by 6 :  

24x - 6y = 66 ………..(3)

On Subtracting equation (2)  from equation (3), we obtain :

24x - 6y = 66

3x - 6y = - 18

(-)  (+)     (+)

------------------

21x = 84

x = 84/21

x = 4

On putting x = 4 in eq (2)  we obtain :  

3x - 6y = - 18

3(4) - 6y = - 18

24 - 6y  = - 18

6y = 18 + 24

6y = 30

y = 30/6

y = 5

Now , fraction =  x/y = 4/5

Hence, the fraction is 4/5.

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

 

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

https://brainly.in/question/17224763

Answer 2

AnsWer :

4/5.

Solution :

°•° Let the Numerator be x

and denominator be y.

So, Fraction is x/y

$\rule{180}1$

A/Q,

Case 1.

When 3 is added to the denominator and 2 is subtracted from the numerator a fraction becomes 1/4.

$\tt\longmapsto \frac{x - 2}{y + 3} = \frac{1}{4}$

$\tt\longmapsto 4(x - 2) = y + 3.$

$\tt\longmapsto 4x - 8 = y + 3.$

$\tt\longmapsto 4x - 11 = y. \: \: \: \: \: - (1)$

$\rule{180}1$

Case 2.

when 6 is added to numerator and the denominator is multiplied by 3, it becomes 2/3

$\tt\longmapsto \frac{x + 6}{3y} = \frac{2}{3}$

$\tt\longmapsto \frac{3(x +6 )}{6y} = 1.$

$\tt \longmapsto 2y = x + 6 \: \: \: \: \: - (2)$

Now, Putting the Equation 1 in 2, We get.

$\tt \longmapsto 2y = x + 6.$

$\tt \longmapsto 2(4x - 11) = x + 6.$

$\tt \longmapsto 8x - 22 = x + 6.$

$\tt \longmapsto 7x = 28.$

$\tt \longmapsto x = 4.$

$\rule{180}1$

Putting the value of x in equation 2, We get.

$\tt \longmapsto y = 4x - 11.$

$\tt \longmapsto y = 4(4) - 11$

$\tt \longmapsto y = 16 - 11.$

$\tt \longmapsto y = 5.$

$\rule{180}1$

• X = 4.
• Y = 5.

=> X/Y = 4/5.

Therefore, Our Fraction become 4/5.