Question

40) The sum of the numerator and denominator of a fraction is 18. If 3 is
subtracted from numerator and 1 is added to the denominator, it becomes
1/3. The fraction is:

Answer 1

Answer:

The fraction is 7/11.

Step-by-step explanation:

Let the numerator and denominator of a fraction be 'a' and 'b' respectively.

Given,

• a/b
• a+b=18

Let a+b=18 be Equation 1.

• (a-3)/(b+1)=1/3

(a-3)/(b+1)=1/3

• (a-3)=1/3(b+1)[b+1 is transposed to the other side]
• a-3=b/3+1/3
• a-3=(b+1)/3
• (a-3)3=b+1[1/3 is transposed to the other side]
• 3a-9=b+1
• 3a=b+1+9[-9 is transposed to the other side]
• 3a-b=+1+9[b is transposed to the other side]
• 3a-b=10

Let 3a-b=10 be Equation 2.

{Equation 1} a+b=18

{Equation 2}3a-b=10

_______

By Adding,

• 4a=28[Elimination by equating coefficients]
• a=28/4[4 is transposed to the other side]
• a=7

{Equation 1}a+b=18

• 7+b=18[a=7]
• b=18-7[7 is transposed to the other side]
• b=11

Verification

a+b=18

7+11

=18

(a-3)/(b+1)=1/3

(7-3)/(11+1)

4/12

=1/3

Hence, verified.

The fraction is 7/11.