21. Walking at 3/4th of his regular speed, Sanjay is 16 minutes late in reaching the office. Find the usual time that he takes to reach the office.
Answer : 48 min.
As distance is equal S1*T1=S2*T2
Let S1 is his usual speed which is X and given `S2=(3X)/4`
22. A train moves at a constant speed of 120 km/hr for one km and at 40 km/hr for the next km. Find the average speed of the train.
Answer : 60 kmph.
Total distance=2 km
so average speed =2/1/30=60
23. A can finish a piece of work in 10, while B can finish it in 20 days. They start working together and after 5 days, A leaves the job. Find the number of days in which B will finish the remaining work.
Answer : 5.
Work done by A in one day is `1/10`
Work done by B in one day is `1/20`
Total work done by A and B in one day is `1/10+1/20=3/20`
Total work done by A and B in 5 days is `5*(3/20)=3/4`
Remaining work is `1-3/4=1/4`
So B will work alone and complete `1/4` work in `(1/4)*20=5` days
24. At what exact time between 5 and 6 will the two hands of a clock be at an angle of 180 degrees
Answer : None of these.
5 o’clock, the hands of the watch are 25 min. spaces apart.
To be in opposite directions, they must be 30 min. spaces apart.
Minute hand will have to gain 25+30=55 min. spaces.
55 min. spaces are gained in 60 min(This is general)
25. An integer is chosen at random from 1 to 100. Find the probability that it is a multiple of 5 or 8.
Answer : 3/10.
26. A ship went on a voyage. After it had traveled 180 miles a plane started with 10 times the speed of the ship. Find the distance when they meet from starting point.
Answer : 200.
27. Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal to the bullets each had after division. Find the original number divided.
Answer : 18.
As there are 3 friends who divides bullets equally the answer should be a multiple of 3.
Use trial and error method
option 1: 24/3=8 afer shooting 4 bullets each will have 4. 4+4+4=12!=8
option 2: 18/3=6 shooting 4 bullets each will have 2. 2+2+2=6
28. A hotel has 10 floors. Which floor is above the floor below the floor, below the floor above the floor, below the floor above the fifth?
Answer : 5th.
Solve this problem from back. First above 5 means 6 then below 6 means 5 then above 5 means again 6 then below 6 means again 5 then below 5 means 4 then above 4 means 5.
29. Two trains starting at same time, one from Bangalore to Mysore and other in opposite direction arrive at their destination 1 hr and 4 hours respectively after passing each other. How much faster is one train from other?
Answer : twice.
Let the time required to reach the meeting point is t,so the meeting point would be at a distance of u*t and v*t from the two stations.
Now according to the given condition u*t = v*4 and v*t = u*1
on taking the ratio of these 2 equations, we have u/v = 4v/u or u/v = 2/1
30. Father’s age is three years more than three times the son’s age. After three years, father’s age will be ten years more than twice the son’s age. What is the father’s present age?
Answer : 33.
Let F=fathers’s present age and S= son’s present age
solve this and you will get F=33