Aptitude Questions

Distance and Time

1. A man covered a certain distance at some speed. Had he moved 3 km/hr faster,
he would have taken 40 minutes less. If he had moved 2 km/hr slower, he
would have taken 40 minutes more. The distance (in km) is:
2. It takes eight hours for a 600 km journey if 120 km is done by train and the rest
by car. It takes 20 minutes more if 200 km is done by train and the rest by car.
The ratio of the speed of the train to that of the car is:
3. In a flight of 600 km, an aircraft was slowed down due to bad weather. Its
average speed for the trip was reduced by 200 km/hr and the time of flight
increased by 30 minutes. The duration of the flight is:
4. A man travels five equal distances of 5 km each at a speed of 5, 10, 20, 30 and
60 km/hr respectively. Find his average speed for the whole journey?
Area
1. The diagonal of the floor of a rectangular closet is 7 feet. The shorter side of
the closet is 4 feet. What is the area of the closet in square feet?
2. A towel, when bleached, was found to have lost 20% of its length and 10%
of its breadth. The percentage of decrease in area is:
3. A man walked diagonally across a square lot. Approximately, what
percentage of distance did he save by not walking along the edges?
4. An error 13% in excess is made while measuring the side of a square. The
percentage of error in the calculated area of the square is?
Series
1. Series: 5, 7, 12, 24, 50, ?
2. Series: 2, 5, 10, 17, 26, ?
3. Series: 3, 6, 18, 144, 2880, ?
4. 7, 8, 18, 57, 232, ?
Time and Work
1. A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how
many days can A do the work if he is assisted by B and C on every third day?
2. A can do a piece of work in 4 hours; B and C together can do it in 3 hours,
while A and C together can do it in 2 hours. How long will B alone take to do
it?
3. A machine P can print one lakh books in 8 hours, machine Q in 10 hours and
machine R in 12 hours. All start at 9 A.M.; P stops at 11 A.M. and the
remaining two finish. At what time is the job done?
4. A, B, and C can do a job in 10 days, 15 days, and 20 days respectively. After
1/12 of the work is completed, C leaves the job. Rest of the work is done by
A and B together. Then what is time taken to finish the work?
Problems on Numbers
1. A number when divided by 5 leaves a remainder 3, and when divided by 7
leaves a remainder 4. What is the smallest such number?
2. The sum of three consecutive odd numbers is 111. What is the middle
number?
3. A two-digit number is such that the product of its digits is 24. If we reverse
the digits, the number decreases by 18. What is the number?
4. The digit sum of a 2-digit number is 8 and the digits are same. What is the
number?
Profit and Loss
1. If selling price is doubled, the profit triples. Find the profit percent.
2. The percentage profit earned by selling an article for Rs. 1920 is equal to the
percentage loss incurred by selling the same article for Rs. 1280. At what
price should the article be sold to make 25% profit?
3. A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of another variety at
Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is?
Mixtures and Alligations
1.A vessel is filled with a mixture of water and syrup in the ratio 3 : 5. A portion
of the mixture is drawn off and replaced with water such that the resulting
mixture is half water and half syrup. What fraction of the mixture was drawn
off?
2.A container initially has a mixture of liquids A and B in the ratio 7 : 5. After
removing 9 L of the mixture and adding pure B, the new ratio becomes 7 : 9.
How many litres of A were there initially?
3.Find the ratio in which rice costing ₹7.20 per kg must be mixed with rice
costing ₹5.70 per kg to produce a mixture worth ₹6.30 per kg.
4. Two liquids A and B are in ratio 4:1 in container X and 3:5 in container Y. In
what ratio should the contents of both containers be mixed so that the
resulting mixture has A and B in ratio 2:3?
Average
Q1.
The average weight of 8 persons increases by 2.5 kg when one person weighing
65 kg is replaced by a new person. What is the weight of the new person?
Q2.
A family consists of two grandparents, two parents, and three grandchildren.
The average age of the grandparents is 67 years, that of the parents is 35 years,
and that of the grandchildren is 6 years. What is the average age of the entire
family?
Q3.
A grocer’s monthly sales for five consecutive months are ₹6435, ₹6927, ₹6855,
₹7230, and ₹6562. How much must he sell in the sixth month so that his
six-month average sales reach ₹6500?
Q4.
In a class, average age of 30 students is 20 years. If the age of 2 more students
is taken into consideration, then the average of all students gets increase by 1.
Find the average of the ages of those 2 students?

Simple Interest
Q1.
Two persons Praveen and Ajay borrowed Rs.30,000/- and Rs.50,000/-
respectively from Raju at different rates of simple interest. The interest payable
by Praveen at the end of the first four years and that payable by Ajay at the end
of the first three years is the same. If the total interest payable by Praveen and
Ajay for one year is Rs.5,250/-, then at what rate did Ajay borrow the money
from Raju?
Q2.
A borrowed ₹8,000 at simple interest. After 2 years, he had to pay ₹1,200
interest. What is the rate of interest per annum?
Q3.
Renu lent ₹6,000 to A for 2 years and ₹8,000 to B for 3 years on simple interest
at the same rate. She received ₹1,440 total interest after the entire period.
What was the rate of interest?
Q4.
An amount invested at simple interest doubles itself in 8 years. How much
interest will ₹5,000 fetch in 5 years at the same rate?
Percentage
Q1.
Population of a country increases every year by 10%. If the population in
January 2006 was 15.8 lakh, what will be the population in January 2008?
Q2.
A quantity is increased by 20% and then decreased by 20%. What is the net
percentage change?
Q3.
An item costs ₹400 and the price is first reduced by 15%, then increased by
15%. What is the net change in the final price?
Q4.
If a country's population increases by 5% in the first year and 10% in the
second year, what is the total percentage increase over two years?
Permutation and Combination
Q1.
From a group of 7 men and 6 women, five persons are to be selected to form a
committee such that at least 3 men are included.
In how many ways can this be done?
Q2.
In how many different ways can the letters of the word ‘LEADING’ be arranged
so that the vowels always come together?
Q3.
From 7 consonants and 4 vowels, how many words of 3 consonants and 2
vowels can be formed?
Q4.
In a box containing 2 white, 3 black, and 4 red balls, how many ways can 3 balls
be drawn if at least one black ball must be included?
Probability
1.A fair coin is tossed, and a fair six-sided die is rolled. What is the probability
of getting a tail and an even number?
2. Two cards are drawn from a well-shuffled pack of 52 cards. What is the
probability that at least one of them is a king?
3. Two dice are thrown. What is the probability that the sum is a multiple of 3?
4. What is the probability that the vowels are always together when the letters
of the word ‘ARTICLE’ are rearranged?
5. A box contains 3 balloons of shape 1, 4 balloons of shape 2 and 5 balloons of
shape 3. Three balloons of them are drawn at random, what is the probability
that all the three are of different shape?
Clock
1.
A watch which gains 5 secs in 3 minutes was right at 7 am. In the Afternoon of
the same day, when the watch indicated quarter past 4 O'clock, the true time
is?
2.
At what time between 4 and 5 o'clock will the hands of a clock be at right
angles?
3.
A clock is set right at 8 a.m. The clock gains 10 minutes in 24 hours. What will
be the true time when the clock indicates 1 p.m. on the following day?
4.
How many times in a day, the hands of a clock are straight?
Pipes
1.
Two pipes B and F can fill the tank in 10 hours and 15 hours, respectively. If
both the pipes are opened along with an outlet pipe M, then the tank is filled
in 30 hours. Find out how much time will the outlet pipe take to empty the full
tank?
2.
Pipes A and B can fill a tank in 5 hours and 6 hours respectively. Pipe C can
empty it in 12 hours. If all three pipes are opened together, in how many hours
will the tank be filled?
3.
A pump fills a tank in 2 hours. Because of a leak, it takes 15/7 hours to fill it.
The leak can drain the full tank in how many hours?
4.
Two inlet pipes can fill a cistern in 37½ minutes and 45 minutes respectively.
Both pipes are opened. The cistern will be full in half an hour if pipe B is turned
off after how many minutes?
Problems on Trains
Q1.
Two stations A and B are 110 km apart. Train A starts from A at 7 a.m. towards
B at 20 km/hr. Train B starts from B at 8 a.m. towards A at 25 km/hr.
At what time will they meet?
Q2.
A train traveling at 75 mph enters a tunnel 3½ miles long. The train itself is ¼
mile long.
Q3.
Two trains running in the same direction have speeds of 40 km/hr and
20 km/hr. The faster train fully passes a man sitting in the slower train in 5
seconds.
Q4.
A train overtakes two people walking in the same direction—one at 4.5 km/hr
and the other at 5.4 km/hr. It takes 8.4 seconds to pass the first person and 8.5
seconds to pass the second.
What is the speed of the train?
Ratio and Proportion
Q1.
The ratio of the number of boys to girls in a college is 7 : 8. If the number of
boys increases by 20% and the number of girls by 10%, what will be the new
ratio?
Q2.
Salaries of Ravi and Sumit are in the ratio 2 : 3. If each of their salaries is
increased by ₹4,000, the new salary ratio becomes 40 : 57. What is Sumit’s
salary?
Q3.
The sum of three numbers is 98. If the ratio of the first to second is 2 : 3 and
that of the second to third is 5 : 8, what is the second number?
Q4.
If A, B, C receive salaries in the ratio 2 : 3 : 5 and they receive increments of
15%, 10%, and 20% respectively, what is the new ratio of their salaries?
Boats and Streams
Q1.
A boat running downstream covers a distance of 16 km in 2 hours, while for
the same distance upstream it takes 4 hours.
What is the speed of the boat in still water?
Q2.
A boatman goes 2 km against the current in 1 hour, and 1 km along the
current in 10 minutes.
How long will it take to go 5 km in still water?
Q3.
A man takes twice as long to row the same distance against the stream as he
does with the stream.
What is the ratio of the speed of the boat (in still water) to the speed of the
stream?
Q4.
A man rows to a place 48 km away and returns in 14 hours. He can row 4 km
downstream in the same time as 3 km upstream.
What is the speed of the stream?
Height and Distance
Q1.
Two ships are sailing on opposite sides of a lighthouse. The angle of elevation
of the top of the lighthouse from the two ships are 30° and 45°, and the
lighthouse height is 100 m.
Find the distance between the two ships.
Q2.
A ladder leaning against a wall makes an angle of elevation of 60° at its base.
The foot of the ladder is 4.6 m away from the wall.
What is the length of the ladder?
Q3.
An observer who is 1.6 m tall stands at a distance of 20320\sqrt{3}203 m from
the base of a tower. The angle of elevation from his eye-level to the top of the
tower is 30°.
What is the height of the tower?
Q4.
From a point on level ground, the angle of elevation of the top of a 100 m high
tower is 30°.
Find the distance of the point from the foot of the tower.