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प्रश्न
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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उत्तर
Let’s assume the fraction be `x/y`
1st condition:
`(x - 2)/y = (1)/(3)`
⇒ 3x – 6 = y
⇒ 3x – y = 6 ...(1)
2nd condition:
`x/(y - 1) = (1)/(2)`
⇒ 2x – y – 1
⇒ 2x – y = –1
Using elimination 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
Hence, the required fraction is `(7)/(15)`.
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