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ICSE Class 9 Answered

A fraction is such that if both the numerator and denominator are increased by unity the fraction becomes 1/2. ,  and if the numerator is doubled and the denominator increased by 2, the fraction becomes 4/5. . Find the fraction
Asked by Jainkarishma76 | 05 Jun, 2019, 11:56: AM
answered-by-expert Expert Answer
Let the fraction be x/y.
If both the numerator and denominator are increased by unity the fraction becomes 1/2.
begin mathsize 16px style fraction numerator straight x plus 1 over denominator straight y plus 1 end fraction equals 1 half
2 straight x plus 2 equals straight y plus 1
2 straight x minus straight y equals negative 1..... left parenthesis straight i right parenthesis end style
The numerator is doubled and the denominator increased by 2, the fraction becomes 4/5.
begin mathsize 16px style fraction numerator 2 straight x over denominator straight y plus 2 end fraction equals 4 over 5
10 straight x equals 4 straight y plus 8
10 straight x minus 4 straight y equals 8
5 straight x minus 2 straight y equals 4..... left parenthesis ii right parenthesis end style
Solving (i) and (ii) we get x=6 and y=13
The fraction is 6/13.
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