25% extra quantity of a commodity

Asked: 25 % extra quantity of a commodity for the same price is equivalent to a discount of what percentage?

Let cost price be c and selling price be s

25 % extra quantity of a commodity means cost price increases to 1.25c

s/1.25c = .8 s/c = (1- .2)s/c

Equivalent to discount of 20%

IMO B

for the given info we need to determine the value of discount on the basic price but there is no change in the said qty of product being purchased
supposedly basic cost of item is $10 per unit so we can purchase 10 units of the same ( 1$ per item)
but now @ $10 we can buy 12.5 units
therefore we can say that the price per unit of item has now become ; 10/12.5 ; $0.8 from $1 ; net ∆ ; 1-.8/1 ; 20% discount
OPTION B

Since this is a percentage change question that doesn't give us any value, we can take 100 as our base value.

Let's say we buy a commodity of 100gm at the cost of $100 (i.e. $1 per gram).

But now we get 25% extra i.e. on 100gm we get an extra of 25% at the same cost. So now we get 125gms for $100.

On a normal day if we needed 125grm we would have spent $125. But since we only spend $100, we are basically given a discount. Now all we need to do is convert this statement in a mathematical one.

It's like saying, what is the percentage decrease on a bill of $125 if only $100 was paid. (IanStewart am I correct with this understanding)

So,
Initial Value = $125 (Original price of the commodity of 125gms)
Finial Value = $100 (Actual price paid for the commodity of 100gms)

Using the percentage decrease formula \(\frac{Initial value - Final value}{Initial value} \)\(* 100\) \(= ?\)

\(\frac{125 - 100}{125}\) \(* 100 \) \(= ?\)

= 20%

Tip: Generally there is a relationship between 25% and 20%. If we increase something by 25% we need to decrease the new value by 20% to get the original value back. If we decrease something by 20% we need to increase the new value by 25% to get the original value.

The above tip can be used in this work/rate question: https://gmatclub.com/forum/it-takes-10- ... 15907.html Notice how statement (1) is actually the same as statement (2)

garcmillan has given a very cool method to go about with it. Learnt something new

Wow! This explanation is pretty cool and easy to remember.

Thanks Man!

\(\frac{25}{(100+25)}*100 = 20%\), Answer must be (B)

Yes, your understanding is perfect. Though as the question is written, it's really possible to justify two different answers:



Say you buy 4 grams of zinc for $4. You're paying $1 per gram. If you instead get 25% more zinc, you're getting 5 grams for $4. So you're paying $0.80 per gram, which is 20% less than $1. So 20% is presumably the answer the question writer intends for the question. But in this precise situation, you were paying $4 to begin with, and you were paying $4 after you got the extra zinc. You haven't gotten a discount of any kind -- you've only gotten more zinc. So you could easily justify the answer "0%" here too, because the question doesn't tell you that it's asking for the discount *per gram* or *per unit* (or whatever would be the relevant way to measure the 'commodity' the question describes). So the question isn't worded precisely enough to be answerable, and you could justify answer B or answer E here depending on how you read it.

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.