A fraction is such that if the numirator is multiplied by 3 and denominator is reduced by 3 we get 18/11 but if the numirator is increased by 8 and the denominator is doubled we get 2/5 . What is the fraction .
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Let the numerator be a, and denominator be b.
Fraction is a/b
According to the question, if numerator is multiplied by 3 and denominator is reduced by 3 We get 18/11
= > 3a/(b-3) = 18/11
= > 33a = 18( b - 3 )
= > 33a = 18b - 54 ...(1)
As well as, when the numerator is increased by 8 and the denominator is doubled, we get 2/5
= > ( a + 8 ) / ( 2b ) = 2/5
= > 5(a+8) = 4b
= > 5a + 40 = 4b
= > 33a(5) + 1320 = 132b
= > 5(18b-54) + 1320 = 132b
= > 90b - 270 + 1320 = 132b
= > 1050 = 42b
= > 25 = b
Therefore, 5a = 4b - 40 = 4(25)-40 = 60
= > a = 12
Hence the required fraction is a/b = 12/25
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