Math, asked by solankiurvashi991, 5 months ago

The numerator of a rational number is 8 less than its denominator If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is
 \frac{21}{25}
Find the originalrational number.

Answers

Answered by Anonymous
22

Answer :-

  • The fraction is 7/15.

Given :-

  • The numerator of a rational number is 8 less than its denominator If the numerator is multiplied by 3 and 10 is added to the denominator the new rational number is 21/25.

To Find :-

  • Original fraction.

Solution :-

Let

  • Denominator be x
  • Numerator will be x - 8

Numerator is multiplied by 3

  • 3 (x - 8)

10 is added to the denominator

  • x + 10

→ New fraction is 21/25

According to question :-

⇒3 (x - 8)/x + 10 = 21/25

⇒3x - 24/x + 10 = 21/25

⇒25 (3x - 24) = 21 (x + 10)

⇒75x - 600 = 21x + 210

⇒75x - 21x = 210 + 600

⇒54x = 810

⇒x = 810/54

⇒x = 15

Now

  • Denominator = x = 15
  • Numerator = x - 8 = 15 - 8 = 7

Hence, the fraction is 7/15.

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