An important and exam oriented question from linear equations in two variables as it was already asked in various examinations in which we have given that when 1 is subtracted from the numerator, the fraction becomes 1/2 and when 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator. And we asked to find the fraction

Kindly solve the above problem

RS Aggarwal, Class 10, chapter 3E, question no 22

Let the required fraction be x/y . Then, we have:

x−1/ y+2 = 1/2

⇒ 2(x – 1) = 1(y + 2)

⇒2x – 2 = y + 2

⇒2x – y = 4 ……(i)

Again, x−7/ y−2 = 1/3

⇒3(x – 7) = 1(y – 2)

⇒3x – 21 = y – 2

⇒ 3x –y = 19 ……(ii)

On subtracting (i) from (ii), we get: x = (19 – 4) = 15

On substituting x = 15 in (i), we get: 2 × 15 – y = 4

⇒ 30 – y = 4

⇒y = 26

∴ x = 15 and y = 26

Hence, the required fraction is 15/26