A and B brought a radio each for the same price, $z. A and B sold thei

Question

A and B brought a radio each for the same price, $z. A and B sold their radio for $x and $y respectively. If x>y>z, A’s profit is what percent greater than B’s?

(1) x – y = 20
(2) x – z = 40

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chetan2u · Answer

A's profit =  \frac{x-z}{z} , and B's profit =  \frac{y-z}{z}

% change of A over B =  \frac{A's.profit-B's.profit}{b"s.profit}*100...........\frac{\frac{x-z}{z}-\frac{y-z}{z}}{\frac{y-z}{z}}*100=\frac{\frac{x-y}{z}}{\frac{y-z}{z}}*100=\frac{x-y}{y-z}*100 ...

Hence, we require values of x, y and z OR values of x-y and y-z

We have some fractions for A’s and B’s profit. When we substitute it in the formula 
 \frac{\frac{(x-z)}{z}-\frac{(y-z)}{z}}{(\frac{y-z}{z})}=\frac{\frac{(x-z-(y-z))}{z}}{\frac{((y-z)}{z)}}=\frac{(x-z-y+z)}{y-z}=\frac{(x-y)}{(y-z)} 
Now we know x-y and y-z can be found from the two statements. 
 Subtract statement I from ii
 (x-z)-(x-y)=40-20=20....y-z=20

Statement I and II give us these values when combined
Answer =  \frac{20}{20}*100=100% 
y-z can be found by subtracting Statement I from statement II

C

pkky · Answer

chetan2u  : I have a doubt, the stmt. 2 says "x-z = 40", I'm wondering how was it substituted into "y-z", please help me with this as I'm stuck at this point when I solved it myself.

kendrikFROMkenya · Answer

Not sure if I agree with the answer;

I think it should be a ratio for percent of A/ B. Not percent change formula as we are not dealing with one item and seeing how they change over time.

Also, I set up the equations like this: PROFIT (A)= REVENUE- COST = X-Z / PROFIT (B) = Y-Z

SO (X-Z)/ (Y-Z). This is the equation to use for both statements.

1) SInce Z is the same and based on profit formula can we conclude that x is 20 % more than y. Sufficeint.

2) 40/ (y-z). Not Suff.

Thanks

chetan2u · Answer

Hi

We have some fractions for A’s and B’s profit. When we substitute it in the formula 
 \frac{\frac{(x-z)}{z}-\frac{(y-z)}{z}}{(\frac{y-z}{z})}=\frac{\frac{(x-z-(y-z))}{z}}{\frac{((y-z)}{z)}}=\frac{(x-z-y+z)}{y-z}=\frac{(x-y)}{(y-z)} 
Now we know x-y and y-z can be found from the two statements. 
 Subtract statement I from ii
 (x-z)-(x-y)=40-20=20....y-z=20

SonamRa · Answer

Although in first go we try to attempt to find values of x,y,z but we need to find difference in profit earned by each
i.e. S.P-C.P. for both
From statement 1 : x-y = 20, doesn't make any sense alone so insufficient
From statement 2 : x-z = 40 imply profit earned by x is 40 but still we have no idea about the profit earned by y to compare both
so statement 2 alone is also not sufficient
now when we combine both:
Substract equation 1 from 2
y-z=20, so now we know the profit earned by y
Now we can easily calculate required percentage

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A and B brought a radio each for the same price, $z. A and B sold thei

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