Q) A fraction becomes when 2 is subtracted from the numerator and it becomes when 1 is subtracted from the denominator- Find the fraction.

Ans: 

Step 1: Let’s consider the fraction be

Step 2: By 1st condition 1: “When 2 is subtracted from the numerator, the fraction becomes “

∴

∴ 3 (x – 2) = y

∴ 3 x – 6 = y

∴ 3 x – y = 6 … .. (i)

Step 3: By 2nd condition: “When 1 is subtracted from the denominator, the fraction becomes “

∴

∴ 2 x = y – 1

∴ 2 x – y = – 1……. (ii)

Step 4: To solve for x & y, let’s subtract equation (ii) from equation (i): 

3 x – y = 6 ………. (i)

2 x – y = – 1 ……….(ii)

∴ (3 x – y) – (2 x – y) = 6 – (- 1)

∴ 3 x – y – 2 x + y = 7

∴ x = 7

Step 5: Substituting value of x in equation (i), we get:

3 x – y = 6

∴ 3 (7) – y = 6

∴ y = 21 – 6

∴ y = 15

Step 6: Substituting values of x and y in assumed frcation, we get:

Final fraction = .

Therefore, the fraction is .

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