Michael planned to spend $600 on renting workshop space for a specific

Question

Michael planned to spend $600 on renting workshop space for a specific number of hours at a certain hourly rate. However, he discovered that the rental rate was $20 higher per hour than he had anticipated. Consequently, he increased his budget to $800, but still ended up renting the space for 10 fewer hours than planned. What was the actual hourly rental rate for the workshop space?

A. 30
B. 35
C. 40
D. 50
E. 60

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Bunuel · Accepted Answer

Official Solution:

Michael planned to spend $600 on renting workshop space for a specific number of hours at a certain hourly rate. However, he discovered that the rental rate was $20 higher per hour than he had anticipated. Consequently, he increased his budget to $800, but still ended up renting the space for 10 fewer hours than planned. What was the actual hourly rental rate for the workshop space?

A. 30
B. 35
C. 40
D. 50
E. 60

Assume the actual hourly rental rate for the workshop space is  p  dollars. Then, at this rate, Michael would have rented the space for  \frac{800}{p}  hours.

The hourly rate at which Michael originally planned to rent the space would be  (p - 20)  dollars, and at this rate, he planned to rent the space for  \frac{600}{p-20}  hours.

Given that the actual rental duration was 10 hours less than planned, we have:
 
 \frac{800}{p} +10 = \frac{600}{p-20} 
 
At this stage, plugging in the answer options to back-solve is easier.

By doing so, we find that option C fits:  \frac{800}{40} +10 = 30  and   \frac{600}{p-20} = 30 .

Answer: C

tgsankar10 · Answer

Actual Hourly rate -  r 
Actual rented hours -  h

Actual scenario:  h*r=800

Estimated scenario: 
 (h+10)*(r-20)=600

hr-20h+10r-200=600

10r-20h=0  (plugging in  h*r=800 )

10r-\frac{20*800}{r}=0  (plugging in  h=\frac{800}{r} )

10r^2-\frac{16000}{r}=0

r^2=1600

r=40

Answer is C.

Purnank · Answer

Assuming x as hourly rate that he had anticipated.
Therefore,
(600/x) - (800/x+20) = 10
600x + 12000 - 800x = 10x^2 + 200x
x^2 + 40x - 1200 = 0
Solving for x = 20, -60
-60 is invalid,
Therefore actual hourly rental rate = x + 20 = 20+20 =40
AnswerC.

VivekSri · Answer

Answer for equation would be x=-60 and 20 and -60 would be invalid.

Purnank · Answer

ohh thanks corrected.

Saksham1224 · Answer

Bunuel  - for this question can we not take the initial r*t = 600, then (r+20)*(t-10)=800? That doesn't seem to give any answer

Bunuel · Answer

rt = 600 and (r + 20)(t - 10) = 800 gives r = 20 and t = 30. Thus, the actual hourly rental rate for the workshop space is r + 20 = 40.

Answer: C.

Vivek1707 · Answer

Testing values instead of algebra can help save time here,

We have the following

xy = 600
(x+20)*(y-10) = 800

Start with x = 10 and y = 60 ---> then x = 30 and y = 50; therefore 30 * 50 is not equal to 800

Next try x = 20 and y = 30 ---> then x = 40 and y = 20 therefore 40 * 20 = 800 Matches perfectly

Hence Answer is 40 i.e C

laborumpossimus · Answer

i made the same equation and tried plugging in the options where did i go wrong

Bunuel · Answer

The equation is fine. The issue is what x represents.

In the solution, x is defined as the  anticipated hourly rate , but the answer choices give the  actual hourly rate .

So you cannot plug the choices directly in for x. For example, if the answer choice is 40, then x = 20 because the actual rate is x + 20.

That gives:

600/20 - 800/40 = 10

30 - 20 = 10

So the actual rate is $40.

Michael planned to spend $600 on renting workshop space for a specific

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GMAT Problem Solving (PS) Questions

Michael planned to spend $600 on renting workshop space for a specific

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

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Perfect 805 Score Debrief by Julia

My Rewards