Question

The numerator of a fraction is 4 less than the denominator. If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction become 15. Find the original fraction.

Answer 1

Corrected Question:-

The numerator of a fraction is 4 less than the denominator. If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction become 1/5. Find the original fraction.

Given :-

→ The numerator of a fraction is 4 less than the denominator.

→ If 1 is subtracted from the numerator and 3 is added to the denominator, the fraction becomes 15.

To find :-

→ The original fraction.

Solution :-

Let the denominator of a fraction be X

The numerator = 4 less than the denominator

The numerator = X-4

The original fraction = (X-4)/X

Condition :-

If 1 is subtracted from the numerator the it will be (X-4-1) = X-5

and If 3 is added to the denominator then it will be X+3

The fraction becomes (X-5)/(X+3)

According to the given problem

The new fraction = 1/5

=> (X-5)/(X+3) = 1/5

On applying cross multiplication then

=> 5(X-5) = X+3

=> 5X-25 = X+3

=> 5X-X = 3+25

=> 4X = 28

=> X = 28/4

=> X = 7

The denominator = 7

The numerator = X-4 = 7-4 = 3

Answer :-

The original fraction is 3/7

Check :-

The numerator = 3

The denominator = 7

The fraction = 3/7

On subtracting 1 from the numerator then it will be 3-1 = 2

On adding 3 to the denominator then it will be 7+3 = 10

The new fraction = 2/10 = 1/5

Verified the given relations in the given problem.

Answer 2

Answer:

Appropriate Question :-

• The numerator of a fraction is 4 less than the denominator. If 1 is substracted from the numerator and 3 is added to the denominator, the fraction becomes 1/5. Find the original fraction.

Given :-

• The numerator of a fraction is 4 less than the denominator.
• If 1 is substracted from the numerator and 3 is added to the denominator, then the fraction becomes 1/5.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf Denominator =\: x$

$\bigstar$ The numerator of a fraction is 4 less than the denominator.

$\mapsto \bf Numerator =\: (x - 4)$

Hence, the original fraction will be :

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

$\leadsto \sf\bold{\blue{Original\: Fraction =\: \dfrac{x - 4}{x}}}$

$\dag$ According to the question :

$\bigstar$ If 1 is substracted from the numerator and 3 is added to the denominator, then the fraction becomes 1/5.

So,

$\implies \bf \bigg\{\dfrac{Numerator - 1}{Denominator + 3}\bigg\} =\: \bigg\{\dfrac{1}{5}\bigg\}$

$\implies \sf \dfrac{x - 4 - 1}{x + 3} =\: \dfrac{1}{5}$

$\implies \sf \dfrac{x - 5}{x + 3} =\: \dfrac{1}{5}$

By doing cross multiplication we get,

$\implies \sf 1(x + 3) =\: 5(x - 5)$

$\implies \sf x + 3 =\: 5x - 25$

$\implies \sf x - 5x =\: - 25 - 3$

$\implies \sf {\cancel{-}} 4x =\: {\cancel{-}} 28$

$\implies \sf 4x =\: 28$

$\implies \sf x =\: \dfrac{28}{4}$

$\implies \sf\bold{\purple{x =\: 7}}$

$\clubsuit$ Required Original Fraction :

$\dashrightarrow \sf Original\: Fraction =\: \dfrac{x - 4}{x}$

$\dashrightarrow \sf Original\: Fraction =\: \dfrac{7 - 4}{7}$

$\dashrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{3}{7}}}$

$\sf\bold{\purple{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{3}{7}\: .}}}$

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