Math, asked by maahira17, 10 months ago

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.

Answers

Answered by nikitasingh79
5

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…

 

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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?

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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.

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Answered by amitkumar44481
5

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.

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