Question

A fraction becomes 1/3 if 1 is subtracted from both it's numerator and denominator. If 1 is added to the both the numerator and denominator,it becomes 1/2. find the fraction

Answer 1

Given :

• A fraction becomes 1/3 if 1 is substracted from both its numerator and denominator .
• If 1 is added to the both the numerator and denominator , it becomes 1/2.

To find :

• The original fraction.

Solution :

Consider,

• Numerator = x
• Denominator = y

According to the 1st condition :-

• A fraction becomes 1/3 if 1 is substracted from both its numerator and denominator.

$\to\sf{\dfrac{x-1}{y-1}=\dfrac{1}{3}}$

$\to\sf{3x-3=y-1}$

$\to\sf{3x=y+2}$

$\to\sf{y=3x-2.........................eq(1)}$

According to the 2nd condition :-

• If 1 is added to the both the numerator and denominator , it becomes 1/2.

$\to\sf{\dfrac{x+1}{y+1}=\dfrac{1}{2}}$

$\to\sf{2x+2=y+1}$

$\to\sf{2x+2=3x-2+1\:[put\:y=3x-2\: from\:eq(1)]}$

$\to\sf{2x-3x=-2+1-2}$

$\to\sf{-x=-3}$

$\to\sf{x=3}$

• Numerator = 3

Now , put x = 3 in eq(1) for getting the value of y.

$\to\sf{y=3x-2}$

$\to\sf{y=3\times\:3-2}$

$\to\sf{y=7}$

• Denominator = 7

Therefore ,

${\boxed{\bold{Original\: fraction=\dfrac{3}{7}}}}$

Answer 2

GIVEN :

•A fraction becomes 1/3 if 1 is subtracted from both it's numerator and denominator.

• If 1 is added to the both the numerator and denominator,it becomes 1/2.

TO FIND :

•The original fraction.

SOLUTION :

=> Consider, Numerator = R and Denominator =S.

•A fraction becomes 1/3 if 1 is subtracted from both it's numerator and denominator.

=> .°. R - 1 / S - 1 = 1 / 3

=> 3(R - 1) = 1(S - 1)

=> 3R - 3 = S - 1

=> 3R = S + 2

=> S = 3R - 2 ............(1)

• If 1 is added to the both the numerator and denominator,it becomes 1/2.

=> R + 1 / S + 1 = 1 / 2

=> 2(R + 1 ) = 1(S + 1)

=> 2R + 2 = S - 1

=> 2R + 2 = 3R - 2 + 1. (°.° S = 3R - 2)

=> 2R - 3R = -2 + 1 - 2

=> - R = - 3

=> R = 3

.° . Numerator = 3

•R = 3 put in equation. (1) ,

=> S = 3(3)-2

=> S = 9 - 2

=> S = 7

.°. Denominator = 7 .

Hence,

Original fraction = 3 / 7 .