Question

Solve the following problems by forming equations ​

Answer 1

Question:-

The denominator of a rational number is greater than its numerator by 4 . If the numerator is increased by 1 and the denominator is increased by 3 , the number obtained is 1/2 . Find the rational number .

♪ Solution:—

$\large \bold{ Let \: the \: rational \: number \: be \: \: \frac{x}{y} }$

Where x is numerator and y is denominator.

★ In the 1st case ,

The denominator of the rational number is greater than its numerator by 4.

→ y - x = 4

→ x - y = - 4 ———(1)

★ In the 2nd case ,

If the numerator is increased by 1 and the denominator is increased by 3 , the number obtained is 1/2.

$\rightarrow \: \large\bold{\frac{x + 1}{y + 3} = \frac{1}{2} }$

$\rightarrow \: \large\bold{(x + 1)2 = y + 3}$

$\rightarrow \: \large\bold{2x + 2 = y + 3}$

$\rightarrow \: \large\bold{2x - y = 1} \: \: \: - - - (2)$

Now , eq(1) - eq(2)↓

→ x - y - (2x - y) = -4 -1

→ x - y - 2x + y = -5

→ -x = -5

→ $\large\boxed{\bold{x\:=\:5}}$

• Putting the value of x in eq(1) , we get ,

• 5 - y = - 4

→ - y = - 4 -5

→ -y = -9

→ $\large\boxed{\bold{y\:=\:9}}$

So, ★ the numerator (x) → 5

and ★ the denominator (y) → 9

$\underbrace{\large \boxed{\bold{★Hence, \: the \: rational \: number \: is \: \: \frac{5}{9} \:★ }}}$

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• This problem is solved with the help of »elimination method«