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1
A driver of a auto rickshaw sees a lorry 60 meters ahead of him. After 30 seconds the lorry is 90 meters behind. If the speed of the auto rickshaw is 38 kmph, then what is the speed of the lorry?
» Explain it
C
 Relative speed = Total distance = 60 + 90 = 5 m/s Total time 30

 ∴   5 m/s = 5 × 18 = 18 kmph 5

Now relative speed = speed of auto rickshaw – speed of lorry

or, 18 = 38 – speed of lorry

∴   Speed of lorry = 38 – 18 = 20 km/h

Hence, option C is correct.
2
There are three athletes A, B and C at a same point. A starts running from a point at a speed of 40 m/min. After 5 minutes, B starts running after A with a speed of 50 m/min. Simultaneously, C also starts running after A at 60 m/min. What distance has C covered (in m) when he catches A?
» Explain it
D
When B started, A is ahead by 40 × 5 = 200 m

But C will catch A before the B as he is faster than the B.

Since A and C run in the same direction, relative speed of C = 60 − 40 = 20 m/min

 ∴  Time taken by C to actually catch A = 200 = 10 mins 20

Distance actually covered by C in this duration = 10 × 60 = 600 m

Hence, option D is correct.

3
Salman was travelling on one side of the Yamuna express way with a constant speed of 120 kmph in his car. Govinda was travelling with a constant speed of 80 kmph in the opposite direction. When they crossed each other, Salman decided to take a U-turn and meet him. But before taking a U turn, Salman had to travel for another 3 minutes. How long will it take for Salman to meet Govinda? [Assume time taken by Salman to take U turn is negligible]
» Explain it
E
Distance Travelled by Salman in 3 minutes
 = 3 × 120 = 6 km 60

Distance travelled by Govinda in 3 minutes
 = 3 × 80 = 4 km 60

Hence Salman will have to travel a distance of 10 km before catching up with Govinda.

Relative speed of Salman to that of Govinda after taking U turn = 120 – 80 = 40 kmph

∴  Time taken by Salman after taking U turn to Meet Govinda = 10/40 = 15 minutes

Total time taken by Salman to meet Govinda = (3 + 15)minutes = 18 minutes

Hence, option E is correct.
4
The taxi charges in a city consist of fixed charges and additional charges per kilometer. The fixed charges are for a distance of up to 5 km and additional charges are applicable per kilometer thereafter. The charge for a distance of 10 km is Rs. 350 and for 25 km is Rs. 800. The charge for a distance of 30 km is-
» Explain it
D
Let the fixed charges = Rs. x (for the first 5 km)

and the additional charges = Rs. y /km

As per the question,

x + 5y = 350 ....(i)

x + 20y = 800 ...(ii)

On solving eqn. (i) and (ii), we get

x = 200, y = 30

∴   Charge for a distance of 30 km.

= x + 25y = 200 + 30 × 25 = Rs. 950

Hence, option D is correct.
5
A Volvo tourist bus with only the driver inside has a speed of 80 kmph. Its maximum speed reduces by a quantity which is directly proportional to the number of passengers (excluding the driver) seated inside. The maximum speed of the bus reduces by 20 kmph, if there are 5 passengers. A maximum of how many passengers should be seated so that the bus can move?
» Explain it
B
If R is the reduction in maximum speed and N is the number of passengers, then R is proportional to N

⇒ R = NK where K is constant of proportionality,

Given data: R = 20, when N = 5, hence K = 4

Maximum number of passenger that bus can’t move = (80 – N × K) = 80 – N × 4 ⇒ N = 20

So number of passenger for bust just move = 20 – 1 = 19

Hence correct option (B) is correct.