Question

When 1 is added to the numerator of the fraction,the fraction becomes 1/2, but when 3 is added to its denominator it becomes 1/3.Find the fraction ​

Answer 1

Answer:5/112

Step-by-step explanation: A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. The fraction is 5/12.

Answer 2

Answer:

Given :-

• When 1 is added to the numerator of the fraction, the fraction becomes 1/2, but when 3 is added to its denominator it becomes 1/3.

To Find :-

• What is the fraction.

Solution :-

Let,

$\mapsto \bf Numerator =\: x$

$\mapsto \bf Denominator =\: y$

Then, the required fraction is :

$\leadsto \sf Required\: Fraction =\: \dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\green{Required\: Fraction =\: \dfrac{x}{y}}}$

According to the question :

$\bigstar$ When 1 is added to the numerator of the fraction, the fraction becomes 1/2.

So,

$\implies \bf \bigg\{\dfrac{Numerator + 1}{Denominator}\bigg\} =\: \bigg\{\dfrac{1}{2}\bigg\}$

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

By doing cross multiplication we get,

$\implies \sf 2(x + 1) =\: y$

$\implies \sf 2x + 2 =\: y$

$\implies \sf\bold{\purple{2x - y =\: - 2\: ------\: (Equation\: No\: 1)}}$

Again,

$\bigstar$ When 3 is added to its denominator it becomes 1/3.

So,

$\implies \bf \bigg\{\dfrac{Numerator}{Denominator + 3}\bigg\} =\: \bigg\{\dfrac{1}{3}\bigg\}$

$\implies \sf \dfrac{x}{y + 3} =\: \dfrac{1}{3}$

By doing cross multiplication we get,

$\implies \sf 3(x) =\: y + 3$

$\implies \sf 3x =\: y + 3$

$\implies \sf\bold{\purple{3x - y =\: 3\: ------\: (Equation\: No\: 2)}}$

Now, by substracted equation no 1 from the equation no 2 we get,

$\implies \bf 3x - y - (2x - y) =\: 3 - (- 2)$

$\implies \sf 3x - y - 2x + y =\: 3 + 2$

$\implies \sf 3x - 2x {\cancel{- y}} {\cancel{+ y}} =\: 5$

$\implies \sf\bold{\blue{x =\: 5}}$

Now, by putting x = 5, in the equation no 1 we get,

$\implies \bf 2x - y =\: - 2$

$\implies \sf 2(5) - y =\: - 2$

$\implies \sf 2 \times 5 - y =\: - 2$

$\implies \sf 10 - y =\: - 2$

$\implies \sf - y =\: - 2 - 10$

$\implies \sf {\cancel{-}} y =\: {\cancel{-}} 12$

$\implies \sf\bold{\blue{y =\: 12}}$

$\dag$ Hence, the required fraction is :

$\dashrightarrow \sf Required\: Fraction =\: \dfrac{x}{y}$

$\dashrightarrow \sf\bold{\red{Required\: Fraction =\: \dfrac{5}{12}}}$

$\sf\bold{\pink{\underline{\therefore\: The\: required\: fraction\: is\: \dfrac{5}{12}\: .}}}$