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प्रश्न
If `x/y = 3(1)/3`, find the value of `(x - 3y)/(2x - 5y)`.
बेरीज
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उत्तर
`x/y = 3(1)/3`
Convert the mixed fraction:
`3(1)/3 = 3 + 1/3`
= `(3 xx 3 + 1)/3`
= `10/3`
`x/y = 10/3`
The expression we need to evaluate is `(x - 3y)/(2x - 5y)`
To express this in terms of `x/y`, divide both the numerator and the denominator by y.
`(x - 3y)/(2x - 5y)`
= `((x -3y)/y)/((2x - 5y)/y)`
= `(x/y - (3y)/y)/((2x)/y - (5y)/y)`
= `(x/y - 3)/(2x/y - 5)`
Substitute `x/y = 10/3` into the simplified expression:
`(10/3 - 3)/(2(10/3) - 5)`
= `(10/3 - 9/3)/(20/3 - 15/3)`
= `(1/3)/(5/3)`
`1/3 xx 3/5`
= `1/5`
The value of `(x - 3y)/(2x - 5y)` is `1/5`
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