Question

22. Find a fraction which becomes (?) when 1 is subtracted from the
numerator and 2 is added to the denominator, and the fraction becomes
(1) when 7 is subtracted from the numerator and 2 is subtracted from
the denominator.​

Answer 1

Answer:

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

Step-by-step explanation:

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