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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")`
1st condition:
`("x" -2)/("y") = (1)/(3)`
⇒ `3"x "- 6 = "y"`
⇒ `3"x" - "y" = 6` ...(1)
2nd condition:
`("x")/("y"-1) = (1)/(2)`
⇒ `2"x" - "y" - 1`
⇒ `2"x" - "y" = -1`
Using elimination method:
Multiplying (2) by -1 and then adding (1) and (2)
⇒ `3"x" - "y" = 6`
⇒ `-2"x" + "y" =1`
⇒ `"x" = 7`
Now, from (1)
⇒ `3"x" - "y" = 6`
⇒ `3 (7) - "y" = 6`
⇒ `21 - "y" = 6`
⇒ `"y" = 15`
Hence, the required fraction is `(7)/(15)`
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