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22. Ram Singh goes to his office in the city, every day from his suburban house.
His driver Gangaram drops him at the railway station in the morning and picks him up in the evening.
Every evening Ram Singh reaches the station at 5 O' Clock.
Gangaram also reaches at the same time.
One day Ram Singh started early from his office and came to the station at 4 O' Clock.
Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early.
How much time did Ram Singh walk?
Let X be the distance between the house and the station let D be the
distance walked by Ram Singh Let S be the speed of the car
so we have 2X/S = 2(X-D)/S + 30
so D/S = 15 Minutes. The car would have taken 15 mins to reach the station. So Ramsingh
walked for 45 Minutes.
23. In a railway station, there are two trains going.
One in the harbour line and one in the main line, each having a frequency of 10 minutes.
The main line service starts at 5 o'clock and the harbour line starts at 5.02A.M.
A man goes to the station every day to catch the first train that comes.
What is the probability of the man catching the main line train?
if he arrives between 5:00 and 5:02 he will take the harbor line train.
if he arrives between 5:02 and 5:10 he will take the main line train.
so probability = 8/10 = 0.8
24. A family X went for a vacation.
Unfortunately it rained for 13 days when they were there.
But whenever it rained in the mornings, they had clear afternoons and vice versa.
In all they enjoyed 11 mornings and 12 afternoons.
How many days did they stay there totally
Total no of non rainy days = (11 + 12 - 13)/2 = 5 days.
Total no of days = 13 + 5 = 18 days.
25. Albert and Fernandes have two leg swimming race.
Both start from opposite ends of the pool.
On the first leg, the boys pass each other at 18 m from the deep end of the pool.
During the second leg they pass at 10 m from the shallow end of the pool.
Both go at constant speed but one of them is faster.
Each boy rests for 4 seconds at the end of the first leg.
What is the length of the pool?
Let L be the length of the swimming pool.
Let S1,S2 be speed of Albert and Fernandez.
so (L-18)/S1 = 18/S2 -- 1
L/S1 + 4 + (L - 10)/S1 = L/S2 + 4 + 10 / S2
(2L -10) / S1 = (L + 10) / S2 -- 2
substituting S1/S2 from 1 and solving 2 we have
L^2 - 44L = 0 or L = 44 Meters
26. Every day a cyclist meets a train at a particular crossing.
The road is straight before the crossing and both are travelling in the same direction.
The cyclist travels with a speed of 10 Kmph.
One day the cyclist comes late by 25 min. and meets the train 5km before the crossing.
What is the speed of the train?
IF he would have come at the correct time he would be 10 * 25 / 60 = 25/6 Kms away from the crossing.
So the time taken by the bicycle to cross 5 - 25/6 Kms is the same as the time taken by the train
to cross 5 kms. So time taken by the boy to cross 5/6 kms is 5/60 hours. Speed of the train is
5 / (5/60) = 60 Kmph
27. Two twins have certain peculiar charcteristics.
One of them always lies on Monday, Wednesday, Friday.
The other always lies on Tuesdays, Thursdays and Saturdays.
On the other days they tell the truth. You are given a conversation.
Person A-- today is Sunday my name is Anil
Person B -- today is Tuesday, my name is Bill
What day is today?
Both of them speak truth on Sunday. So A cannot be true if B claims differnt.
so A is lying so he should be of type who lies on Tuesdays, Thursdays and Saturdays.
B is the guy who lies on Monday, Wednesday, Friday.
so the day is tuesday.
His driver Gangaram drops him at the railway station in the morning and picks him up in the evening.
Every evening Ram Singh reaches the station at 5 O' Clock.
Gangaram also reaches at the same time.
One day Ram Singh started early from his office and came to the station at 4 O' Clock.
Not wanting to wait for the car he starts walking home. Mangaram starts at normal time, picks him up on the way and takes him back house, half an hour early.
How much time did Ram Singh walk?
Let X be the distance between the house and the station let D be the
distance walked by Ram Singh Let S be the speed of the car
so we have 2X/S = 2(X-D)/S + 30
so D/S = 15 Minutes. The car would have taken 15 mins to reach the station. So Ramsingh
walked for 45 Minutes.
23. In a railway station, there are two trains going.
One in the harbour line and one in the main line, each having a frequency of 10 minutes.
The main line service starts at 5 o'clock and the harbour line starts at 5.02A.M.
A man goes to the station every day to catch the first train that comes.
What is the probability of the man catching the main line train?
if he arrives between 5:00 and 5:02 he will take the harbor line train.
if he arrives between 5:02 and 5:10 he will take the main line train.
so probability = 8/10 = 0.8
24. A family X went for a vacation.
Unfortunately it rained for 13 days when they were there.
But whenever it rained in the mornings, they had clear afternoons and vice versa.
In all they enjoyed 11 mornings and 12 afternoons.
How many days did they stay there totally
Total no of non rainy days = (11 + 12 - 13)/2 = 5 days.
Total no of days = 13 + 5 = 18 days.
25. Albert and Fernandes have two leg swimming race.
Both start from opposite ends of the pool.
On the first leg, the boys pass each other at 18 m from the deep end of the pool.
During the second leg they pass at 10 m from the shallow end of the pool.
Both go at constant speed but one of them is faster.
Each boy rests for 4 seconds at the end of the first leg.
What is the length of the pool?
Let L be the length of the swimming pool.
Let S1,S2 be speed of Albert and Fernandez.
so (L-18)/S1 = 18/S2 -- 1
L/S1 + 4 + (L - 10)/S1 = L/S2 + 4 + 10 / S2
(2L -10) / S1 = (L + 10) / S2 -- 2
substituting S1/S2 from 1 and solving 2 we have
L^2 - 44L = 0 or L = 44 Meters
26. Every day a cyclist meets a train at a particular crossing.
The road is straight before the crossing and both are travelling in the same direction.
The cyclist travels with a speed of 10 Kmph.
One day the cyclist comes late by 25 min. and meets the train 5km before the crossing.
What is the speed of the train?
IF he would have come at the correct time he would be 10 * 25 / 60 = 25/6 Kms away from the crossing.
So the time taken by the bicycle to cross 5 - 25/6 Kms is the same as the time taken by the train
to cross 5 kms. So time taken by the boy to cross 5/6 kms is 5/60 hours. Speed of the train is
5 / (5/60) = 60 Kmph
27. Two twins have certain peculiar charcteristics.
One of them always lies on Monday, Wednesday, Friday.
The other always lies on Tuesdays, Thursdays and Saturdays.
On the other days they tell the truth. You are given a conversation.
Person A-- today is Sunday my name is Anil
Person B -- today is Tuesday, my name is Bill
What day is today?
Both of them speak truth on Sunday. So A cannot be true if B claims differnt.
so A is lying so he should be of type who lies on Tuesdays, Thursdays and Saturdays.
B is the guy who lies on Monday, Wednesday, Friday.
so the day is tuesday.
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