Question

2. Find a fraction which becomes (1/2) when 1 is subtracted from the
numerator and 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.
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Answer 1

Answer:

Let the numerator be cans denominator be y

fraction=x/y

⇒x-1/y+2=1/2

⇒2x-2=y+2

⇒2x-y=4.... ..(1)

⇒x-7/y-2=1/3

⇒3x-21=y-2

⇒3x-y=19........(2)

⇒2x-y=4

⇒3x-y=19

⇒-x=-15

⇒x=15

put x=15 in equation (1)

⇒2x-y=4

⇒2x15-y=4

⇒30-y=4

⇒-y=4-30

⇒-y=-26

⇒y=26

Step-by-step explanation:

Answer 2

Step-by-step explanation:

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