Question

a fraction becomes 2/3 when 1 is subtracted from the numerator and it becomes 1/2 when 7 is added to the denominator. find the fraction

Answer 1

Hi,

Here
Let the fraction be
x/y

So,
It is given that
x - 1/y = 2/3
x = 2/3 y
x = 2/3 y +1


Now we have got the value of x = 2/3y + 1

Now,
In second case

x/y + 7 = 1/2
Now put the value of x
So,

2/3y + 1/ y + 7 = 1/2
Cross Multiply the number

2( 2/3 y + 1) = 1 (y +7)
4/3 y + 2 = y + 7
4/3 y - y = 7-2
1y/3 =5
y = 15

Therefore y = 15
So,

x = 2/3 y + 1
x =2/3 ×15 + 1
x = 10 +1
x =11

Therefore our fraction was x/y
= 11/15


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