Question

Find a fraction which become 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 from denominator.

Answer 1

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

putx=15 in equation (1)

2x-y=4

2x15-y=4

30-y=4

-y=4-30

-y=-26

y=26

Hope it helps you

Have a great day

Answer 2

Answer: $\dfrac{15}{26}$

Step-by-step explanation:

Let the fraction be $\dfrac{x}{y }$

Now, According to the question:-

$\dfrac{x-1}{y+2}=\dfrac{1}{2}\\\\\Rightarrow\ 2(x-1)=y+2\\\\\Rightarrow\ 2x-2=y+2...............................(1)$

$\dfrac{x-7}{y-2}=\dfrac{1}{3}\\\\\Rightarrow3(x-7)=(y-2)\\\\\Rightarrow\ 3x-21=y-2.................................(2)$

Now subtracting (1) from (2), we get

$x-19=-4\\\\\Rightarrow x=-4+19=15$

Put x=15 in (1), we get

$y+2=2(15)-2=28\\\\\Rightarrow\ y=26$

Hence, the required fraction is $\dfrac{15}{26}$.