# the sum of numerator and denominator of fraction is 4 more than twice the numerator.if the numerator and denominator are increase by 3 they are in the ratio 2:3.find the fraction

• 5

Let the numerator be x and the denominator be y.

1. x + y = 4+2y

x = 4 - y  ...(i)

2. x+3 / y+3 = 2 / 3

3x - 2y = -3 ..(ii)

Now, by substituting the value of x from (i) in eq (ii) we get,

3 (4-y) -2y = -3

y = 3

Now, substituting the value of y in eq. (i) we get,

x = 4 - 3

x = 1

So, the fraction is x / y = 1/3

• 2
 Let the numerator be x and the denominator be y. 1. x + y = 4+2y x = 4 - y ...(i) 2. x+3 / y+3 = 2 / 3 3x - 2y = -3 ..(ii) Now, by substituting the value of x from (i) in eq (ii) we get, 3 (4-y) -2y = -3 y = 3 Now, substituting the value of y in eq. (i) we get, x = 4 - 3 x = 1 So, the fraction is x / y = 1/3
• 4

hi kunalX,  you have taken x + y= 4 + 2y , where you have supposed numerator to be x and denominator as y. Thus, by your equation  you mean that the sum of numerator and denominator is equal to four more than twice of DENOMINATOR,  but in the question it is actually that the sum of numerator and denominator is four more than twice the NUMERATOR  hence by changing the values there will be a different answer than what u have found...

• 6

now , here is the answer :--

Let the numerator be x and denominator be y. A/Q  x + y = 4 + 2x    ==>  - x + y = 4  ...(1)  multiplying each term by 2,  2x-2y= -8 ....(2) Also, (x+3) / (y+3) = 2 / 3  ==> 3x - 2y = -3 ........(3)                                                                                                                                     Subtracting (2) from (3) ==> x=5 and by putting this in (1) we can get y=9.  Hence, the fraction is   5 / 9

• 67
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