Question

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.​

Answer 1

Question:

A fraction becomes 1/3 when 2 is subtracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator. Find the fraction.

Answer:

7/15

Solution:

Let the numerator and the denominator of the fraction be N and D respectively.

Thus ,

The required fraction will be N/D .

Now,

It is given that ;

The fraction becomes 1/3 when 2 is subtracted from the numerator.

Thus,

=> (N-2)/D = 1/3

=> 3•(N-2) = 1•D

=> 3N - 6 = D --------(1)

Also,

The fraction becomes 1/2 when 1 is subtracted from the denominator.

Thus,

=> N/(D-1) = 1/2

=> 2•N = 1•(D-1)

=> 2N = D - 1

=> 2N + 1 = D --------(2)

Now,

From eq-(1) and eq-(2) , we have;

=> 3N - 6 = 2N + 1

=> 3N - 2N = 6 + 1

=> N = 7

Now,

Putting N = 7 , in eq-(2) , we get ;

=> 2N + 1 = D

=> 2•7 + 1 = D

=> 14 + 1 = D

=> D = 15

Hence,

The required fraction is N/D ie; 7/15

Answer 2

Answer:

$\bold\green{Fraction=\frac{7}{15}}$

_______________________

Let the numerator be X

And the denominator be Y

1.According to question:-

=> (X-2)/Y = 1/3

=> Y = 3X - 6..............(ii)

2.According to question :-

=> X/(Y-1) = 1/2

=> 2X = Y - 1

=> Y = 2X + 1........(ii)

Putting the value of (i) here,

=> 3X - 6 = 2X + 1

=> 3X - 2X = 1+6

=> X = 7

Numerator = 7

Denominator = 2 × 7 + 1 = 15

________________________

Fraction = 7/15

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