number one:
As the stamps are in the ratio 5:3
say kaye has 5x and alberto has 3x. then after kaye gave 10 stemps to alberto.
kaye= 5x-10
alberto=3x+10 and the new ratio is 7:5
solve this: 5x-10/3x+10=7/5 u will get x=30.

the difference in the stemps is 5(30)-3(30)=60

the Answer is D 60.

number two :

6*12 = 72 machine-days are required.
let x machines will finish the job in 8 ,then total 8x machine-days are required.
8x=72 -- x=9
therefore 3 additional machines are required.

Answer is B

ans are C,B respectively

ok. I misread the last line.we have to tell the number of stamps after kay gave 10 stemps to alberto.
as we have solved x=30.
Kay has 5x-10= 140 stamps
Alberto has 3x+10= 100 stamps

difference is 40 stamps.
Answer is c

Thanks! I thought in the first problem that the equation was 5x-10/3x+10=7y/5y and couldn't solve the problem under 2 mins. Does anyone know why we add a variable to the second part of the ratio equation in some problems and not in others? I'm unclear on that.