Question

A fraction becomes 1/2 when 3 is subtracted from its numerator. If 5 and 7 are respectively added to its numerator and denominator, it becomes 3\4 then, the LCM of the numerator and denominator of the said fraction,must be

Answer 1

let the original fraction be a/b

equation #1:
(a - 3)/b = 1/2
b = 2a - 6

equation #2:
(a+5)/(b+7) = 3/4
4a + 20 = 3b + 21
4a - 3b = 1
sub in #1
4a - 3(2a-6) = 1
4a-6a+18 = 1
-2a = -17
a = 17/2
b = 2(17/2)-6 = 11

our fraction is (17/2)/11 = 17/22

When we check with 17/22, we fail
When we check with (17/2) / 11 it works
that is:
(17/2 - 3)/11 = 1/2
(17/2 + 5)/(11+7) = 3/4

but for 17/22, which is the same as (17/2) / 11
if we have (17-3)/22 ≠ 1/2
and (15+5)/(22+7) ≠ 3/4

They should have specified to take the fraction in its
original complex form

Answer 2

johnny
diggie
biggums