# A man reaches his office 30 minutes late if he walks by $\frac{2}{3}$rd of his routine speed. What is the time he usually takes to reach office?

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A man reaches his office 30 minutes late if he walks by $\frac{2}{3}$rd of his routine speed. What is the time he usually takes to reach office?
1. 30 minutes
2. 60 minutes
3. 90 minutes
4. 45 minutes

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Correct Answer - Option 2 : 60 minutes

Given:

The man reaches the office late by 30 minutes

Formula used:

Distance = Speed × Time

Concept used:

Speed is inversely proportional to the time taken

Calculation:

Let the distance from the office and home be x and original speed be y

Then, the Original time is taken = x/y

Decreased speed = 2y/3

Time is taken when speed is decreased = Distance/Speed = x/(2y/3)

Now, A/Q

x/(2y/3) – x/y = 30

⇒ 3x/2y – x/y = 30

⇒ x/2y = 30

⇒ x/y = 30 × 2 = 60 minutes

∴ The actual time is taken by the man to reach the office is 60 minutes