Question: By walking at 4/5th of his usual speed, Brent reaches his office 10 minutes later than usual. What is the usual time taken by Brent to reach his office?

1. 15 minutes
2. 20 minutes
3. 40 minutes
4. 45 minutes
5. 55 minutes

Answer:
Solution with Expalnation:
Approach Solution (1):

As we know distance is constant in this scenario so, speed is indirectly proportional to Time
Speed ratio is 4/5 means initially speed 5
New speed = 4
Initial speed = 4 (inverse relationship)
New speed = 5
Difference of time is given 10 minutes late
1 = 10 minutes
So initial time = 4 * 10 = 40 minutes

Correct Option: C

Approach Solution (2):

Given: The person walks 4/5 of the usual speed
He was 10- minutes later than usual
Formula used: Distance = Speed * Time
Calculation: Let the distance covered be D and his speed be S
So, his usual time to reach the office = \(\frac{D}{S}\)
Now, his new speed = \(\frac{4}{5}S\)
According to the question:

\(\left\{\frac{\frac{D}{4S}}{5}\right\} - \left\{\frac{D}{S}\right\} = 10 minutes\)
\(\Rightarrow\frac{5D}{4S}-\frac{D}{S} = \frac{10}{60}hours\)
\(\Rightarrow \frac{D}{4S}=\frac{1}{6}hours\)
\(\Rightarrow \frac{D}{S} = \frac{4}{6}hours\)
\(\Rightarrow \left\{\frac{4}{6}* 60\right\} minutes = 40 minutes\)

Correct Option: C

Approach Solution (3):

Formula used: \(Speed \propto \frac{1}{Time}\)
Calculation:
Usual speed : New speed = 5 : 4
Usual time : New time = 4 : 5
So, the difference between usual time to new time = ( 5 – 4) units = 1 unit
Now, 1 unit = 10 minutes
4 units = (10 * 4) minutes
= 40 minutes

Correct Option: C

“By walking at 4/5th of his usual speed, Brent reaches his office 10 minutes later than usual. What is the usual time taken by Brent to reach his office?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.

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