Shortcut Trick
When time is constant, the distance travelled is directly proportional to the speed (D ∝ S).
Ratio of speeds = 10 : 12 ⇒ 5 : 6.
Ratio of distances = 5 : 6.
Difference in distance = 6 − 5 = 1 unit.
According to the question, 1 unit = 1 km, so actual distance = 5 units = 5 km.
∴ The correct answer is 5 km.
Alternate Method
Given:
Actual speed = 10 km/hr
New speed = 12 km/hr
Difference in distance = 1 km
Formula:
Time = Distance ÷ Speed
Let the actual distance travelled be D km.
⇒ Time taken at 10 km/hr = D ÷ 10
⇒ Time taken at 12 km/hr = (D + 1) ÷ 12
⇒ Since the time is the same in both cases:
⇒ D ÷ 10 = (D + 1) ÷ 12
⇒ 12 × D = 10 × (D + 1)
⇒ 12D = 10D + 10
⇒ 12D − 10D = 10
⇒ 2D = 10
⇒ D = 10 ÷ 2 = 5 km
∴ The correct answer is 5 km.
Additional Information
Relationship between Speed, Distance and Time
Speed is defined as the rate at which an object covers distance. Formula: Speed = Distance ÷ Time.
Direct Proportionality Case
When Time is constant, Distance (D) is directly proportional to Speed (S). Ratio formula: D1/D2 = S1/S2.
Inverse Proportionality Case
When Distance is constant, Speed (S) is inversely proportional to Time (T). Ratio formula: S1/S2 = T2/T1.
Average Speed Formula
If a person covers the same distance at two different speeds x and y, the Average Speed = 2xy ÷ (x + y).
∴ The correct answer is 5 km.