A fraction reduces by 4/5 when 2 is subtracted from the numerator and 3 is addded to the denominator.But it reduces to 12/17 if 6 is added to the numerator and the denominator is multiplied by 2.Find the fraction?
Answers
Given:
A fraction reduces by 4/5 when 2 is subtracted from the numerator and 3 is addded to the denominator.
But it reduces to 12/17 if 6 is added to the numerator and the denominator is multiplied by 2.
To find:
Find the fraction?
Solution:
Let the fraction be x/y
From given, we have,
(x - 2)/(y + 3) = 4/5
⇒ 5x - 4y = 22 ......(1)
(x + 6)/(2y) = 12/17
⇒ 17x - 24y = -102 .....(2)
solving equations (1) and (2), we get,
x = 18 and y = 17
Therefore, the required fraction is 18/17
Given: A fraction reduces by 4/5 when 2 is subtracted from the numerator and 3 is added to the denominator.But it reduces to 12/17 if 6 is added to the numerator and the denominator is multiplied by 2.
To find: Find the fraction?
Solution:
- Now according to the question:
- Let the numerator be x and denominator be y.
- Then the required fraction will be:x/y
- For first condition, we have:
x − 2 / y + 3 = 4/5
5x - 10 = 4y + 12
4y = 5x - 22 ........(1)
- For second condition, we have:
x + 6 / 2y = 12/17
17x + 102 = 24y
17x = 24y - 102 ......(2)
- Putting the value of x from (1) in (2), we get:
4y = 5(24y - 102 / 17) - 22
68y = 120y - 510 - 204
714 = 52y
y = 13.730
- Putting the value of x in 1, we get:
4(13.730) = 5x - 22
54.9230 = 5x - 22
54.9230 + 22 = 5x
76.9230 = 5x
x = 76.9230/5
x = 15.3846
x/y is 15.3846 / 13.730.
Answer:
So the value of x/y is 15.3846 / 13.730.