The balance of a trader weighs 10% less than it should. Still the

Question

The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?

A. 40%
B. 8%
C. 25%
D. 16.66%
E. 9%

KarishmaB · Accepted Answer

The most natural way to deal with 'weights' questions is by assuming values.

Say the trader's balance shows 100 gms. It is actually 90 gms because it weighs 10% less. Say, the cost price is $90 ($1/gm). Since he gets a profit of 20%, the selling price must be 90+(20/100)*90 = $108

Since the cost price is actually supposed to be $100 (for 100 gms) and the selling price is $108, the mark up is simply 8%.

syh244 · Answer

IMO - B.

Original cost before weight adjustment: X
Cost after 90% weight adjustment: 9/10X
20% profit on 9/10X: (120/100)(9/10)(X) or 108X/100
Mark up on original cost of X: (108X/100)/X-1 = 8/100

bb · Answer

If OA is B, why did you not mark it when you posted the question and instead put "OA not provided?"

MrGolfer · Answer

I am bit confused here.

Question reads “The balance of a trader weighs 10% less than it should.”
I guess this means the balance of the trader weighs 90gms when the actual weight is 100gms.

Assuming original cost price = c and marked up selling price =s
90 x s = 100 x (120% x c) ---- Here LHS is the cash made by selling 90gm at selling price
 ---- Here RHS is what the seller actually intends i.e. selling the 100gm at 120% of original cost price.

90s =120c
s/c =12/9
s=1.33c

Hence the original price has to be jacked up by 33.33 % to get the intended profit.

P.S - I am solving purely looking at the question. The underlined portion substantiates my doubt. 
The balance of a trader weighs 10% less than it should.  Still the trader marks up his goods  to get an overall profit

KarishmaB · Answer

'Balance weighs 10% less than it should'

What this actually means is that if the balance shows 100 gms, it should weigh 100 gms of produce. But it weighs only 90 gms of produce (10% less).
So you pay for 100 gms but you get to buy only 90 gms.

MrGolfer · Answer

I would differ here.
Question reads “The balance of a trader weighs 10% less than it should.” which implies “The balance of a trader weighs 10% less than it should  .” i.e. 90gm when it should weigh 100gm. And taking it further "Still the trader marks up his goods to get an overall profit of 20%. What is the mark up on the cost price?"

I guess a lot us are working backwards to fit in the answer choice. I guess knowing the source of the question will be great help.

@upasanadatta - Please advise the source of the question.

GMATmission · Answer

I agree with MrGolfer here. I think the profit should be on 100 and not 90. Even I got 33.33%. Source and OE (if possible) please.

fluke · Answer

Bad wording. I think the markup is 20% as mentioned in the stem.
OR, the question should say;
What is the mark up on the SUPPOSED cost price as Karishma mentioned.

Either way; bad question.

KarishmaB · Answer

I guess if many people are troubled by the wording, it must be one of those questions where the wording implies different things depending on your background. I wouldn't worry about such a question.

That said, defective balance/weight questions are often worded in one of these ways:
1. The 1 kg weight weighs 10% less. (Here the weight is the metal piece which is supposed to weigh a kg and is put on one pan of the beam balance. So the product you want to buy is in the other pan and you will get only 900 gms though you will pay for 1 kg)
2. The balance weighs 10% less than it should. I think of a spring balance here. It displays 1 kg but weighs only 900 gms of the product.
3. The balance reads 10% more than what it weighs. Here, if the product is 100 gms, the balance reads 110 gms and you pay for 110 gms.

Also, marked price is always on what is visible to all. The defect in the balance is an anomaly and leads to extra profit for the trader. Otherwise, when he marks up, he does that on what the balance reads.

But as I said, if you have learned it differently, don't worry. In GMAT, it will be very clear what the intended meaning is.

arnoorichenna · Answer

Thanks for explaining.

Dreaming · Answer

@bb: you see, this is precisely why i didnt mark the official answer....ppl have a tendency to 'backsolve' when the answer is known..
@MrGolfer: My thought process more or less followed the same path as yours....but i agree with Karishma's explanation...and also the fact that the wording is not clear in the question.....the OE is same as Karishma's but but not half as clear. The source is a book meant for MBA entrance exams here in India and not really a GMAT practice material...its name is Quantum CAT by Sarvesh Verma ....bad english but an excellent book otherwise....

Kinshook · Answer

Given: The balance of a trader weighs 10% less than it should. Still the trader marks up his goods to get an overall profit of 20%. 
Asked: What is the mark up on the cost price?

Let the mark up on the cost price be x.
1/.9*(1 + x) = 1.2
(1+x) = 1.2*.9 = 1.08
x = 8%

IMO B

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