PERCENTS

[Gurpinder]

OG Problem:

The selling price of an article is equal to the cost of
the article plus the markup. The markup on a certain
television set is what percent of the selling price?
(1) The markup on the television set is 25 percent
of the cost.
(2) The selling price of the television set is $250.

OA: [spoiler](A)[/spoiler]

Please explain!

[Rahul@gurome]

Solution:
Let the selling price be sp, cost price be cp and mark up price be mp.
Or sp = cp + mp.
Consider first (1) alone.
mp = 25% * cp = 0.25cp.
Or sp = cp + 25%cp = 1.25*cp.
Or mp/sp = 0.25cp/1.25cp = 1/5
In % it is 1/5*100 = 20%.
Or (1) alone is sufficient.

Next consider (2) alone.
sp is $250.
But we know nothing about cp and mp.
Or (2) alone is not sufficient.

The correct answer is hence (A).

[Gurpinder]

Solution:
Let the selling price be sp, cost price be cp and mark up price be mp.
Or sp = cp + mp.
Consider first (1) alone.
mp = 25% * cp = 0.25cp.
Or sp = cp + 25%cp = 1.25*cp.
Or mp/sp = 0.25cp/1.25cp = 1/5
In % it is 1/5*100 = 20%.
Or (1) alone is sufficient.

Next consider (2) alone.
sp is $250.
But we know nothing about cp and mp.
Or (2) alone is not sufficient.

The correct answer is hence (A).

Hey rahul,

I understand that Smt 2 is not sufficient. But I just want to confirm whether i get stmt 1:

s=c+m
to get the percentage of m, simply (m/s)(100)

Smt1:

m=.25c

so if, s=c+m ------> s=c + .25c ---> s=1.25c

so .25c/1.25c = 1/5(100).

20%

am i doing this right?

[Rahul@gurome]

Yes! What you did is correct.

[Gurpinder]

Yes! What you did is correct.

Thanks for your help!