Question

the sum of the numerator and denominator of a fraction is greater by 1 than thrice the numerator.if the numerator is decreased by 1 then the fraction to 1/3.find the fraction​

Answer 1

Step-by-step explanation:

let fraction be n/d

n+d =1+3n => d=1+2n

n-1/d =1/3 => 3n-3=d

1+2n = 3n-3

4=n

d=1+2×4=9

fraction =4/9

Answer 2

Answer:

Given :-

The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator is decreased by 1 then the fraction reduced to 1/3.

To Find :-

What is the fraction.

Solution :-

Let, the fraction be x/y

According to the question,

➣ The sum of numerator and denominator of a fraction is greater by 1 than thrice the numerator.

⇒ x + y = 3x + 1

⇒ y = 3x - x + 1

⇒ y = 2x + 1 .......... equation no (1)

➣ Denominator is decreased by 1 than the fraction reduced by 1/3.

⇒ x - 1/y = 1/3

⇒ 3(x - 1) = y

⇒ 3x - 3 = y

⇒ 3x - y = 3 ......... equation no (2)

➣ Now, putting the value of x from equation no (1) in equation no (2) we get,

⇒ 3x - y = 3

⇒ 3x - (2x + 1) = 3

⇒ 3x - 2x - 1 = 3

⇒ x = 3 + 1

➠ x = 4

➣ Again, putting the value of x in the equation no (1) we get,

⇒ y = 2x + 1

⇒ y = 2(4) + 1

⇒ y = 8 + 1

➥ y = 9

Hence, the required fraction will be,

↦ x/y

➽ 4/9

∴ The fraction will be 4/9 .