If the price of a chocolate bar is doubled, by what percent will sales

Question

If the price of a chocolate bar is doubled, by what percent will sales (quantity sold) of the chocolate bar decrease? Assume a direct inverse proportional relationship between price increase in cents versus sales decrease by percentage.

(1) For every 15 cent increase in price, the sales (quantity sold) will decrease by 10%

(2) Each chocolate bar now costs 99 cents

(1) For every 15 cent increase in price, the sales (quantity sold) will decrease by 10%

(2) Each chocolate bar now costs 99 cents

chetan2u · Answer

Lets work out the INFO given..

Initial price =  P_i and later price = P.... P = 2P_i 
and Initial quantity =  Q_i and later quantity = Q....

Given

P_i*Q_i =k* P*Q

P_i*Q_i = 2*P_i*Q*k

Q_i=2Q*k

\frac{Q}{Q_i} = \frac{1}{2k}

We are looking for  \frac{Q_1-Q}{Q_i}= 1- \frac{Q}{Q_i} .

So we are looking for value of k or  \frac{Q}{Q_i}  ..

lets see the statements-

(1) For every 15 cent increase in price, the sales (quantity sold) will decrease by 10%  
 P_i*Q_i =k* P*Q

P_i*Q_i = (P_i+15)*1.15*Q_i*k

P_i=(P_i+15)*1.15*k

P_i=P_i*1.15*k+15*1.15*k .

P_i(1-1.15*k) = 15*1.15*k

P_i = \frac{15*1.15*k}{1-1.15k}

the equation will have two variables P_i and k...
Insuff

(2) Each chocolate bar now costs 99 cents  
we know the ratio as 1/2 and othing about k or quantity..
Insuff

Combined-  
we know P_i as 49.5 cents and P as 99 cents from statement II...
Statement I gives us an equation in terms of k and P_i....
subsitute the value of P_i in  P_i = \frac{15*1.15*k}{1-1.15k} , we will get k..

Suff

C

psdhali · Answer

"Assume a direct inverse proportional relationship between price increase in cents versus sales decrease by percentage" does this not imply that if we get the actual cents by which the price increased that we would know the percentage decrease in the sales?

So for me B would be the answer. (Each chocolate bar now costs 99 cents => original value was 99/2=49.5 cents => 49.5 cents change => 49.5% percent decrease?)

pranjal14 · Answer

Direct inverse proportional relationship doesn't imply that 1 cent increase in price leads to 1% decrease in sales.

Even if we assume that it implies that then the first statement contradicts it.

So I will stick with choice C.

Sent from my A0001 using Tapatalk

pallaviisinha · Answer

Hi Bunuel,

Please provide your explanation of arriving at the correct answer.

Thanks,
Pallavi

ligeraks · Answer

Bunuel wrote:
If the price of a chocolate bar is doubled, by what percent will sales (quantity sold) of the chocolate bar decrease? Assume a direct inverse proportional relationship between price increase in cents versus sales decrease by percentage.

(1) For every 15 cent increase in price, the sales (quantity sold) will decrease by 10%

(2) Each chocolate bar now costs 99 cents
--------------------------------------------------------
Let 'P' be the price increase in cents, 'a' be the initial price of the chocolate in cents and 'n' be the corresponding percentage decrease.

A/Q: P = k/n where k is a constant

(A) 15 = k/10 => k = 150

As the price is doubled, the price basically increases by 'a' cents. Therefore:-

a = k/n = 150/n or n = 150/a

As a is not known, Not Sufficient

(B) 2a = 99 => a = 49.5. Not Sufficient alone

(A) + (B) -> Sufficient. Option C

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If the price of a chocolate bar is doubled, by what percent will sales

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If the price of a chocolate bar is doubled, by what percent will sales

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