P and Q walk from A to B, a distance of 27 km at 5km/hr and 7 km/hr respectively. Q reaches B and immediately turns back meeting P at T. What is the distance from A to T?
Answer: B Let the distance a km from A. So total distance travelled by P = a at a peed of 5km/hr. Total distance travelled by Q = 27+(27-a) = (54-a) at a speed o 7 km/hr. Total time taken by P = a/5 and that by Q = (54-a)/7. Since they have met at the same time, they would have travelled for the same time. Hence, a/5 = (54-a)/7 => a= 22.5 km.
Q. No. 8:
A bus without stopping travels at an average speed of 60 km/hr and with stoppages at an average speed of 40 km/hr. What is the total time taken by the bus for stoppages on a route of length 300km?
Answer: C Let r = running time of the train s= stoppage time of the train D= total distance travelled by train We have, D/r = 60 and D/(r+s) = 40 => (r+s)/r =3/2 => s/r = 1/2 As, D= 300 kms 300/r = 60 => r= 5 hrs and s= 2.5 hr.
Q. No. 9:
A ball is projected vertically upwards reaches, at the end of 't' seconds, an elevation of 's' feet where s= 160t-16t2. The highest elevation is
Answer: C Given that, s= 160t-16t2 Highest value of S will be reached when dS/dt =0 => 160-32t = 0 => t=5 sec Thus S= (160*5) - (16*5*5) = 800 - 400 = 400.
Q. No. 10:
Distance between the points is P. A man with the speed of s and reaches the other point late by 2 hours. Calculated the speed with which the man has to travel to reach in time, where t is the actual time.
Answer: C Assume x be the actual speed. Then p/x = t and p/s = t+2 So, x*t = s*(t+2) => x = s*(t+2)/t
Q. No. 11:
The Ghaziabad-Hapur-Merut EMU and the Meerut-Hapur-Ghaziabad EMU start at the same timefrom Gahaziabad and Meerut and proceed towards each other at 16 km/hr and 21 km/hr respectively.When they meet, it is found that one train has traveled 60 km more than the other. Thedistance between two stations is:
Answer: B The two trains start simultaneously. Let they meet after a time ‘t’. The train that has covered 60 km more must be the faster of the two. Hence, 60 = (21 – 16) × t => t = 12 hours. Since they are traveling towards each other, total distance is the sum of the distances traveled by the two trains individually. Total distance = 16 × 12 + 21 × 12 = 444 Km. Hence (B) is the correct option.
Q. No. 12:
A boat goes 30 km. upstream and 44 km. downstream in 10 hours. In 13 hours, it can go 40 km upstream and 55 km down-stream. The speed of the boat in still water is:
Answer: C If B = speed of boat in still water R = speed of stream Then as per the question: 30/(B-R) + 44/(B+R) = 10 ................(i) 40/(B-R) + 55/(B+R) = 13.................(ii) On solving both the equations we get, B= 8km/hr.