A company decreased the price of its main product by 50%

Question

A company decreased the price of its main product by 50%. Subsequently, the number of units sold increased such that the total revenue remained unchanged. What was the ratio of the percent increase in the units sold to the percent decrease of the original price for this product? 
 
A. 0.5 
B. 1.0 
C. 1.5 
D. 2.0 
E. 4.0

GyanOne · Answer

For the total revenue to remain the same when the price is halved, the number of products sold must double. Therefore increase in the number of products sold is 100%

=> The required ratio = 100%/50% = 2.0

Option (D)

manalq8 · Answer

Thank you good and easy one. for some reason i couldn't solve it, maybe i was stressed while taking the test. thanks again

calreg11 · Answer

Price decreased so quantity must increase so the net effect of the 50% decrease and % increase in quantity must equal 1. And that is 200% increase. We are looking for the net % increase which is 100% increase and then take the ratio of that which is 100%/50% = 2. 
D

Bunuel · Answer

Nice explanation above by GyanOne.

One can also use plug-in method: consider the price of the product to be $10 and the units sold at that price to be 1 --> revenue=$10*1=$10;

If we decrease the price by 50% from $10 to $5 then in order the revenue to remain the same 2 units must be sold which is 100% increase in sales (from 1 to 2).

Hence the ratio is 100%/50%=2.

Answer: D.

Abhii46 · Answer

In such questions it is always easier to chose random values and solve the question.

fukirua · Answer

I used algebraical approach:
1) p1=p2
We know that p1q1=p2q2, let's apply here condition (1) ===> 2p2q1=p2q2. It means that 2q1=q2 or q2/q1=2
Manhattan CAT2 consider this question 700-800 which is not true.

sarahmichalmoore · Answer

I'm confused. Can someone please help me understand why the ratio is 100/50? I get that the quantity halved and the price doubled. But I don't get why the final ratio is a 2 instead of a 1.

This is my reasoning with number:

Initial price= 100
Initial Units=100
x=new quantity

(100)(100)=10,000
(.5)(100)(x)=10,000
x=200 (new quantity)

Quantity percent increase= 
(200-100/100)(100)=100% increase

Price decrease=
(100-50/50)=100% decrease

100/100=1

I know this is wrong, but can someone please help me understand why?

Bunuel · Answer

Is the price decrease from 100 to 50 a 100% decrease? It's 50% decrease: (100-50)/100=0.5.

Hope it's clear.

sarahmichalmoore · Answer

yes it is. I made a very silly mistake. Thank you so much for clarifying!

unceldolan · Answer

I also used an algebraic approach:

initial revenue: p * u = r (p = price; u = units; r= revenue)

now we have a decrease of 0.5 in p and an increase of x in u. r remains the same:

0.5p * (x*u) = r

now equalize:

0.5p * (x*u) = p * u ==> p/0.5p = x*u/u ==> 0.5p=x ==> x = 2 --> here's our ratio!

dunno if this it the right approach but it worked for me lol.

ash99 · Answer

Revenue = Price of product * Units sold

Old - $1000 = $100 * 10

New - $1000 = $50 * 20

Percent decrease of price of product = (100 - 50)/100 *100 = 50

Percent increase of units sold = (20 - 10)/10 *100 = 100

Required ratio = 100/50 = 2 (Answer choice D)

mbaapp1234 · Answer

Smart numbers are the best solution to this problem.

If we start with PQ =4 and P =2 and Q =2, then we know that P becomes 1 and Q becomes 4. 4/2 = 1 = 100% growth for Q whereas we know that P decreased by 50%.

100%/50% = 2.0 or 200%, the ratio of the increase in quantity to the decrease in price (elasticity of the good).

laddaboy · Answer

Initial Price = p , Units sold = A Revenue1 = A*P
New price = p/2 , Units Sold = B Revenue2 = (B*P)/2

From the prompt Revenue 1 = Revenue 2 => 2*A = B => 100% increase in products sold
Required ratio = 100%/ 50% = 2.0

shashankism · Answer

Let the price of product be Rs. 100. It is decreased by 50% to Rs. 50 
Let the no. of products initially sold be 10 and after price decrease be 10k.

So, (100)(x) = (50)(10k)
k = 2

So, after price decrease 20 nos. of products are sold.

So, increase in sale = (20-10)/10 = 100%
Decrease in price= 50%

Ratio = 100/50 = 2.0

Answer D

ScottTargetTestPrep · Answer

Since the company decreased the price of its product by 50% = 1/2, in order to keep the revenue the same, the number of units sold would need to be 2 times what was sold previously, or a 100% increase, which is 1.

Thus, the ratio of the percent increase in units sold to the percent decrease in price is:

(1)/(1/2) = 2

Answer: D

bv8562 · Answer

Original Price = p
No. of units sold = n

Revenue = Price * No. of units sold = p*n

Decreased Price = 0.5p
No. of units sold = n+k

Revenue = 0.5p*(n+k)

Since, both the times the revenue remained the same:

p*n = 0.5p*(n+k)

n:k = 1:1

When the Price was p, the no. of units sold were = n = 1
When the Price was 0.5p, the no. of units sold were = n+k = 1+1 = 2

% increase in the no. of units sold = 1/1*100 = 100%

Ratio = No. of units sold/% decrease of price = 100%/50% = 2 (D)

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A company decreased the price of its main product by 50%

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