Type 8: Actual Speed Fraction

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Q. A person travels at 3/4 of his actual speed and reaches his destination 20 minutes late. If he travels at 5/4 of his actual speed, he reaches 12 minutes early. Find the actual time taken to reach the destination.

Solution:

Let the actual time be T hours.

First condition:

T/3/4 − T = 20/60 

4T/3 − T = 1/3

T/3 = 1/3

T/3 = 1 hour

Second condition:

T − T / 5/4 = 12/60 

T − 4T/5 = 1/5

T/5 = 1/5

T = 1 hour

Therefore,

Ans: 1 hour

Maths Trick:

If speed is k times the actual speed: Actual Time = Late Time/ 1/k − 1 

For speed greater than actual speed: Actual Time = Early Time/1 − 1/k

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TYPE 8: Actual Speed Fraction — Practice Set

Q1. A person travels at 3/4 of his actual speed and reaches 20 minutes late. If he travels at 5/4 of his actual speed, he reaches 12 minutes early. Find the actual time.

(A) 45 min  (B) 60 min  (C) 75 min  (D) 90 min

Q2. A man travels at 4/5 of his actual speed and reaches 15 minutes late. If he travels at 6/5 of his actual speed, he reaches 10 minutes early. Find the actual time.

(A) 45 min  (B) 50 min  (C) 60 min  (D) 75 min

Q3. A student walks at 5/6 of his actual speed and reaches school 12 minutes late. At 10/9 of his actual speed, he reaches 6 minutes early. Find the actual time.

(A) 50 min  (B) 60 min  (C) 72 min  (D) 90 min

Q4. A person travels at 2/3 of his actual speed and reaches 30 minutes late. If he travels at 3/2 of his actual speed, he reaches 20 minutes early. Find the actual time.

(A) 45 min  (B) 60 min  (C) 75 min  (D) 90 min

Q5. A man travels at 5/6 of his actual speed and reaches 18 minutes late. If he travels at 5/4 of his actual speed, he reaches 9 minutes early. Find the actual time.

(A) 72 min  (B) 90 min  (C) 108 min  (D) 120 min

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