Linear Equation 25

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If the numerator of a fraction is decreased by 1, its value becomes 2 /3, but if the denominator is increased by 5,
its value becomes 1 / 2. What is the fraction ?

Solution: Let the fraction be x / y

Therefore, (x - 1) / y = 2 / 3 and x / (y + 5) = 1 / 2

=> 3 x - 3 = 2 y and 2 x = y + 5

=> 3 x - 2 y = 3 and 2 x - y = 5

On solving, we get : x = 7 and y = 9

Therefore, the required fraction = 7 / 9

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