Question

If we add 10 to both terms of a fraction it becomes equivalent to 2/5 if we subtract 5 from both terms of the same fraction it will be equivalent to 3/10 what is this fraction

Answer 1

Let the fraction be a/b, then (a+10)/(b+10)=2/5, 5(a+10)=2(b+10)

5a+50=2b+20, 5a-2b+30=0, -10a+4b-60=0.

Also, (a-5)/(b-5)=3/10, 10(a-5)=3(b-5), 10a-50=3b-15, 10a-3b-35=0.

Add the two equations: b-95=0, so b=95, 10a=3b+35=285+35=320, a=32.

So the original fraction is 32/95.

CHECK: 42/105=6/15=2/5; 27/90=3/10.