BANK & INSURANCE (SPEED TIME AND DISTANCE) PART 2

Total Questions: 45

41. Car A covers D km with the speed of 80 kmph in (t + 3) hours and car B covers (D + 220) km in (2t + 1) hours. If the speed of car B is 25% more than the speed of car A, then find the value of t?

Correct Answer: (d) 3 
Solution:

D/80 = t + 3
D = 80t + 240
(D + 220)/(80 × 125/100) = 2t + 1
D + 220 = 200t + 100

D = 200t - 120
80t + 240 = 200t - 120
120t = 360
t = 3

42. A bus covers a certain distance in 5 hours. If the speed of the bus is reduced by 8kmph, then the same distance is covered in 13 hours. Find the distance covered by the bus with the actual speed in 4 hours?

Correct Answer: (b) 52 km 
Solution:Let total distance be x km
speed = Total distance / Total time
x/5 - x/13 = 8
(13x - 5x)/65 = 8
8x/65 = 8
x = 65 km
Actual speed = 65/5 = 13 kmph
Required distance = 13 × 4 = 52 km

43. A train covers 560 km in 7 hours. The speed of a car is 50% more than the speed of the train. If the train covers D km in (x + 3.5) hours and the car covers the same distance in x hours, then find the value of D?

Correct Answer: (d) 840 km 
Solution:

Speed of train = 560/7 = 80 kmph
Speed of car = 80 × 150/100 = 120 kmph
D/80 = (x + 3.5)
80 × (x + 3.5) = D
D/120 = x
D = 120x

80x + 280 = 120x
x = 7
D = 120 × 7 = 840 km

44. A car is traveling with the speed of 60 kmph and the car increases its speed by 20 kmph after every hour. Find the time taken by the car to cover 360 km?

Correct Answer: (b) 4 
Solution:Sₙ = (n/2) × (2a + (n - 1) × d)
360 = (n/2) × (2 × 60 + (n - 1) × 20)
720 = 120n + 20n² - 20n
n² + 5n - 36 = 0
n² + 9n - 4n - 36 = 0
n(n + 9) - 4(n + 9) = 0
n = 4 hours (Neglecting the negative value)

45. Person X start from point A and person Y start from point B running towards each other and meets first time after 8 hours. (Both are started running at same time). Find speed of Y in km/h, if speed of X is 200% more than Y and distance between A and B is 960 km.

Correct Answer: (c) 30 km/h 
Solution:Let speed of Y = a km/h
Speed of X = 300% of a = 3a
According to question
960/8 = (3a + a)
4a = 120
a = 30
Speed of Y = 30 km/h