25% extra quantity of a commodity

Question

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

A) 15%
B) 20%
C) 25%
D) 30%
E) Information is insufficient to reach a unique answer

Loser94 · Accepted Answer

Lets assume commodity be 100 units
25% more to it will make it 125 units
price of commodity charged is for 100 units(Let say 1 unit price is 1USD)=100USD
so price for 125units will be 125USD
so Discount is 25USD on 125 unit commodity
Discount %=25/125=1/5=20%

Answer B

garcmillan · Answer

Hi all,

This is a very good question that has to do with a percentage increase and a subsequent decrease to result in no change.

If we want to solve it quickly, we should know that the percentage increase would be different that its subsequent decrease to result in no change. For example:

X * 3/2 * 2/3 = X. The percentage increase is 3/2 = 150/100 =  50%  and the decrease is 1-2/3 = 1/3 =  33.3% . As you see after applying a 50% increase and a subsequent 33.3% decrease, the value would still be the same (the percentages are different though)

So, basically this question is asking us to find the decrease percentage that would result in no change. The percentage increase is 25%, which is the same as multiplying the original value by 1.25 = 5/4. Therefore the decrease would be 4/5, which would be a percentage decrease of 1-4/5 = 1/5 =  20%

ANSWER B

Please remember this way to find percentage increase and subsequent percentage decrease to result in no change, as I believe it is pretty straightforward and easy to remember

Kinshook · Answer

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

Archit3110 · Answer

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

Fighter1095 · Answer

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

Thanks Man!

Abhishek009 · Answer

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

Hoozan · Answer

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

IanStewart · Answer

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.

Ghoskrp3 · Answer

25% extra comes at 100% Price means in fractions: \frac{1}{5} th of 125% and \frac{1}{5} th of anything is 20% in percentage terms!

So, B. 20%

25% extra quantity of a commodity

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25% extra quantity of a commodity

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