Speed, Time and Distance
 A man travelled a distance of 61 km in 9 hours, partly on foot at the rate of 4 km/hr and partly on bicycle at the rate of 9 km/hr. The distance travelled on foot was

 12 km
 16 km
 20 km
 24 km

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Let man walked for t hours.
then, t × 4 + (9 – t) × 9 = 61
⇒ 4t + 81 – 9t = 61
⇒ 81 – 5t = 61
⇒ 5t = 20
⇒ t = 4
∴ Distance travelled on foot
= 4 × 4 = 16 km.Correct Option: B
Let man walked for t hours.
then, t × 4 + (9 – t) × 9 = 61
⇒ 4t + 81 – 9t = 61
⇒ 81 – 5t = 61
⇒ 5t = 20
⇒ t = 4
∴ Distance travelled on foot
= 4 × 4 = 16 km.
 Ravi and Ajay start simultaneously from a place A towards B, 60 km apart. Ravi’s speed is 4 km/hr less than that of Ajay. Ajay, after reaching B, turns back and meets Ravi at a place 12 km away from B. Ravi’s speed is

 12 km/hr
 10 km/hr
 8 km/hr
 6 km/hr

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Let the speed of Ravi be x kmph
then, Ajay’s speed = (x + 4) kmph
Distance covered by Ajay
= 60 + 12 = 72 km
Distance covered by Ravi
= 60 – 12 = 48 km.
According to the question,72 = 48 x + 4 x ⇒ 3 = 2 x + 4 x
⇒ 3x = 2x + 8
⇒ x = 8 kmphCorrect Option: C
Let the speed of Ravi be x kmph
then, Ajay’s speed = (x + 4) kmph
Distance covered by Ajay
= 60 + 12 = 72 km
Distance covered by Ravi
= 60 – 12 = 48 km.
According to the question,72 = 48 x + 4 x ⇒ 3 = 2 x + 4 x
⇒ 3x = 2x + 8
⇒ x = 8 kmph
 P and Q are 27 km away. Two trains with speed of 24 km/hr and 18 km/hr respectively start simultaneously from P and Q and travel in the same direction. They meet at a point R beyond Q. Distance QR is

 126 km
 81 km
 48 km
 36 km

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Let the trains meet after t hours, then
24t – 18t = 27
⇒ 6t = 27⇒ t = 27 6 = 9 hours 2 ∴ QR = 18t = 18 × 9 = 81 km 2 Correct Option: B
Let the trains meet after t hours, then
24t – 18t = 27
⇒ 6t = 27⇒ t = 27 6 = 9 hours 2 ∴ QR = 18t = 18 × 9 = 81 km 2
 From two places, 60 km apart, A and B start towards each other at the same time and meet each other after 6 hours.
and B travelled with double of his speed, they would have met after 5 hours. The speed of A isHad A travelled with 2 of his speed 3

 4 km/hr.
 6 km/hr.
 10 km/hr.
 12 km/hr.

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Let the speed of A = x kmph and that of B = y kmph
According to the question,
x × 6 + y × 6 = 60
⇒ x + y = 10 ....(i)and, 2 x × 5 + 2y × 5 = 60 3
⇒ 10x + 30y = 180
⇒ x + 3y = 18 ...(ii)
From equations (i) × (3) – (ii)
3x + 3y – x – 3y = 30 – 18
⇒ 12x = 12
⇒ x = 6 kmph.Correct Option: B
Let the speed of A = x kmph and that of B = y kmph
According to the question,
x × 6 + y × 6 = 60
⇒ x + y = 10 ....(i)and, 2 x × 5 + 2y × 5 = 60 3
⇒ 10x + 30y = 180
⇒ x + 3y = 18 ...(ii)
From equations (i) × (3) – (ii)
3x + 3y – x – 3y = 30 – 18
⇒ 12x = 12
⇒ x = 6 kmph.
 A man completed a certain journey by a car. If he covered 30% of the distance at the speed of 20km/hr, 60% of the distance at 40km/hr and the remaining distance at 10km/hr; his average speed for the whole journey was

 25 km/hr
 28 km/hr
 30 km/hr
 33 km/hr

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Let the total distance be 100 km.
Average speed = Total distance covered Time taken = 100 3 + 3 + 1 2 2 = 100 3 + 3 + 2 2 = 100 × 2 = 25 kmph 8 Correct Option: A
Let the total distance be 100 km.
Average speed = Total distance covered Time taken = 100 3 + 3 + 1 2 2 = 100 3 + 3 + 2 2 = 100 × 2 = 25 kmph 8