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Question
A fraction becomes `1/3` when 2 is subtracted from the numerator and it becomes `1/2` when 1 is subtracted from the denominator. Find the fraction.
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Solution
Let's assume the fraction be `"x"/"y"`
First condition:
`(X-2)/y =1/3`
⇒ 3x -6 = y
⇒ 3X - Y= 6 ............. (1)
second condition:
`x/(y-1)= 1/2`
⇒ 2x = y- 1
⇒ 2x - y = -l ............ (2)
Using eliminated method:
Multiplying : (2) by -1 and then adding (1) and (2)
⇒ 3x- y = 6
⇒ - 2x + y = 1
⇒ x = 7
Now, from (1),
⇒ 3x - y =6
⇒ 3(7) - y = 6
⇒ 21 - y =6
⇒ y = 15
∴ x = 7, y = 15
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