Math, asked by ghoshsujata899, 5 months ago

the the numerator of a fraction is less than its denominator by 4. if if denominator is decreased by 1 and the numerator is increased by 11 the new number becomes 7 by 3 find the original fraction please guys help me please please please​

Answers

Answered by khashrul
5

Answer:

The original fraction = \frac{3}{7}

Step-by-step explanation:

Let's assume the denominator of the fraction is x

∴ The numerator is x - 4.

New denominator = x - 1

And New numerator = x - 4 + 11 = x + 7

According to the problem:

\frac{x + 7}{x - 1} = \frac{7}{3}

=> 3x + 21 = 7x - 7

=> - 4x = -28

∴ x = 7 = original denominator

Original numerator = x - 4 = 3

∴ The original fraction = \frac{3}{7}

Answered by prince5132
7

GIVEN :-

  • The numerator of a fraction is less than its denominator by 4.
  • Denominator is decreased by 1 and the numerator is increased by 11 the new number becomes 7/3.

TO FIND :-

  • The original Fraction.

SOLUTION :-

Let the denominator of the fraction be "x". Therefore the numerator of the fraction be "x - 4".

★ Original Fraction = (x - 4)/x

★══════════════════★

New numerator become x - 6 + 11 = "x + 7".

New denominator become = "x - 1".

★ New fraction = (x + 7)/(x - 1)

 \underline { \bigstar  \: \textsf{According to the Question now :}} \\  \\

: \implies \displaystyle \sf \:  \frac{x + 7}{x - 1}  =  \frac{7}{3}  \\  \\  \\

: \implies \displaystyle \sf \:  7(x - 1) = 3(x + 7) \\  \\  \\

: \implies \displaystyle \sf \:  7x - 7 = 3x + 21 \\  \\  \\

: \implies \displaystyle \sf \:  7x - 3x = 21 + 7 \\  \\  \\

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

: \implies \displaystyle \sf \:  x =  \frac{28}{4}  \\  \\  \\

: \implies \underline{ \boxed{ \displaystyle  \sf \: \textbf{  x = 7}}} \\  \\

★══════════════════★

★ Original Fraction = (x - 4)/x

★ Original fraction = (7 - 4)/7 = 3/7

Hence the required original fraction is 3/7.

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