Annual salary

[alex.gellatly]

In 1994, Kenneth's annual salary was 30 percent higher than it was in 1993. In 1995, Kenneth's annual salary was reduced to 104 percent of his 1993 annual salary. Kenneth's 1995 annual salary was what percent less than his 1994 salary?

A. 16%
B. 20%
C. 24%
D. 26%
E. 28%

[tutorphd]

1993 salary = x
1994 salary = 1.30 x
1995 salary = 1.04 x

change = 1995 salary - 1994 salary = - 0.26 x (negative because it decreased)

percent change with respect to 1994 salary = change/ 1994 salary = 0.26x / 1.30x = 0.26/1.30 = 0.20 = 20%

The 1993 salary x does not matter, it cancel out. If you prefer picking numbers to simple algebra, you could pic a number for x, say x=100 and go through the same motions

[Anurag@Gurome]

In 1994, Kenneth's annual salary was 30 percent higher than it was in 1993. In 1995, Kenneth's annual salary was reduced to 104 percent of his 1993 annual salary. Kenneth's 1995 annual salary was what percent less than his 1994 salary?

Say, annual salary in 1993 = 100
Hence, annual salary in 1994 = 130
And, annual salary in 1995 = 104

Hence, required percentage = 100*(130 - 104)/130 = 100*26/130 = 20

The correct answer is B.

[alex.gellatly]

Both of you are clear and I understand now. However, when I first solved the problem I didn't understand how/why this is a percentage change question. No where in the question does it ask for precentage change. That is why I got ans. D (130-104). How do we know it is asking for percentage change?

Thanks

[Anurag@Gurome]

No where in the question does it ask for precentage change. That is why I got ans. D (130-104). How do we know it is asking for percentage change?

Because the question is asking "Kenneth's 1995 annual salary was what percent less than his 1994 salary? "

[Scott@TargetTestPrep]

In 1994, Kenneth's annual salary was 30 percent higher than it was in 1993. In 1995, Kenneth's annual salary was reduced to 104 percent of his 1993 annual salary. Kenneth's 1995 annual salary was what percent less than his 1994 salary?

A. 16%
B. 20%
C. 24%
D. 26%
E. 28%

Solution:

If the salary in 1993 was n, then the salary in 1994 was 1.3n, and in 1995 1.04n, thus:

(1.30n - 1.04n) / 1.30n x 100

0.26 / 1.30 x 100 = 0.2 x 100 = 20%

Alternate Solution:

Assume that Kenneth’s salary in 1993 was $100. Then, in 1994, it was 100 x 1.3 = $130, and in 1995 it was 100 x 1.04 = $104.

We use the percent less than formula to obtain:

(104 - 130) / 130 x 100

-26/130 x 100

-26/13 x 10

-2 x 10 = -20%, which indicates 20% less.

Answer: B