# Walking at 45% of his usual speed, a man reaches his destination 1 hour 50 minutes late. Find the usual time to reach the destination:

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Walking at 45% of his usual speed, a man reaches his destination 1 hour 50 minutes late. Find the usual time to reach the destination:
1. 2 hr
2. 3 hr
3. 1 1/2 hr
4. 2 1/2 hr

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Correct Answer - Option 3 : 1 1/2 hr

Given:

Speed = 45% = 9/20

Time = 1 hour 50 min = 11/6

Formula used:

Speed = Distance/Time

Speed is inversely proportional to time

Calculation:

Let the speed of the man be 20x

45% of the speed = 20x × 9/20

⇒ 9x

Ratio of speed of man before and after = 20x : 9x

As we know that, speed is inversely proportional to time

Time ratio of man before and after = 9x : 20x

According to the question

⇒ 20x/9  x = 1 hr 50 min = (1 + 50/60) hr

⇒ 11x/9 = 11/6

⇒ 11x = 11 × 9/6

⇒ 11x = 33/2

⇒ x = 3/2 hr

⇒ 1 1/2 hr

∴  The usual time to reach the destination is 1 1/2 hr