Bank- Afcat- NDA - CDSE Aptitude test coaching given by Defence Academy Coimbatore
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Q1. A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)
A. 700
B. 350
C. 1000
D. 4200
ANSWER: A. 700
Solution: A boat travels at the speed of 14 km/hr in still water.
=> Speed of stream = 1.2 kmph
=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph
=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph
Total time taken in the journey = Journey downstream + Journey upstream
Therefore, 4864(1/12.8 + 1/15.2) = 700 hours
Q2. In how many different ways can a group of 4 be made out of 4 girls and 6 boys such that at least one boy is selected each time?
A. 159
B. 209
C. 201
D. 212
Q3. 20% of A is B, then B% of 20 is same as what?
A. 4% of A
B. 10% of A
C. 20% of A
D. None
ANSWER: A. 4% of A
Solution: It is given that B measures 20% of A
=> So, 20% of A = B or 20/100 * A = B - (1)
B% of 20= B/100 X 20= 2B/10 ---(2)
=> Now, B% of 20
Substituting (1) in (2) we get
2*(2A/10) / 10= 4A/100
Hence, B% of 20 = 4% of A
Q4. With an investment of 45000, X starts a business which is joined by Y after 3 months with 30000. How should they share the profit at the end of the year?
A. 1:3
B. 2:1
C. 1:3
D. 3:1
ANSWER: B. 2:1
Solution: Let us consider the relationships here:
Time and Profit ---------------Direct Relationship ---- More time More profit
Investment & Profit ------Direct Relationship ---- More investment More profit
Ratio of profit = Investment * Time of Investment
= 45000 * 12 : 30000 * 9
= 2:1
Q5. A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?
A. 28L
B. 29L
C. 29.16L
D. 28.4L
ANSWER: C. 29.16L
Solution: In regard to the problem let after n times liquid in the container is x and liquid removed is y
=>Liquid in container= x
=>Liquid removed= y
After one trial, quantity of pure liquid= x- (1-y/x)
After n trials quantity of pure liquid = x - (1 -y/x)n
Therefore, Putting the values ( x = 40L y = 4L N=3) and solving
=> 40- (1-4/40)3
= 29.16L
Q6. The cost price of a particular amount of articles is same as the number of articles. Selling price of the articles comes out to be 20. Over the whole transaction 25% is gained. What is X?
A. 15
B. 18
C. 16
D. 20
ANSWER: C. 16
Solution: According to the question let n be the number of articles.
=> Cost price of n articles = n
=> Selling price of n articles = 20
=> Profit % = 25%
=> Profit % = (SP - CP)/CP X 100
Putting the values in the formula
(20-n)/n x 100 = 25
=> 5n/4 = 20
=> n = 16
Q7. Three coins are tossed. What is the probability of getting at most two tails?
A. 7/8
B. 1/8
C. 2/8
4. 4/8
ANSWER: A. 7/8
Solution: It is given that 3 coins are tossed simultaneously.
=>Total outcomes when one coin is tossed=2
=>Total outcomes when 3 coins are tossed= 2n = 2 X 2 X 2
=8 outcomes
Favourable outcomes: TTH, THT, HTT, THH, THT,HHT,HHH=7
Therefore, Probability= 7/8
Q8. A pump fills a tank in 2 hours. Due to a leak it took 2 2/3 hours to fill the tank. In how much time will the leak drain the entire tank?
A. 6 hours
B. 8 hours
C. 9 hours
D. 10 hours
ANSWER: B. 8 hours
Solution: It is given that tank is filled in 2 hours. Let tank drain out in y hours
=> Part of the tank filled in one hour = 1/2
=> Part emptied in one hour by leak = 1/y
=>Part filled in one hour following leak = 1/ (8/3)
In one hour: 1/2 - 1/7 = 3/8
Therefore, Solving for y, y=8
Q9. For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
A. 26m
B. 32m
C. 24m
D. 28m
ANSWER: B. 32m
Solution: This is a simple speed time problem. Given conditions:
=>Speed of P= 224/28 = 8m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 4 seconds
Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres
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Aptitude model placement papers with solution - set 1
Q1. A boat has a speed of 14kmph in standing water. The stream has a speed of 1.2kmph. What time does the boat take to go to a distance of 4864 km and come back? (hours)
A. 700
B. 350
C. 1000
D. 4200
ANSWER: A. 700
Solution: A boat travels at the speed of 14 km/hr in still water.
=> Speed of stream = 1.2 kmph
=> Speed of boat downstream becomes 14 + 1.2 = 15.2 kmph
=> Speed of boat upstream becomes 14 - 1.2 = 12.8 kmph
Total time taken in the journey = Journey downstream + Journey upstream
Therefore, 4864(1/12.8 + 1/15.2) = 700 hours
Q2. In how many different ways can a group of 4 be made out of 4 girls and 6 boys such that at least one boy is selected each time?
A. 159
B. 209
C. 201
D. 212
ANSWER: B. 209
Solution: This solution can be determined by 2 ways. Include at least one boy in each group and make 4 cases. A simpler way would be finding out total ways of selecting 4 people from the total group and subtracting the case with no boy.
=> Group of 4 out of 10 children - Group of 4 out of 4 girls.
=> 10C4 - 4C4
=> 210 - 1
=> 209
Solution: This solution can be determined by 2 ways. Include at least one boy in each group and make 4 cases. A simpler way would be finding out total ways of selecting 4 people from the total group and subtracting the case with no boy.
=> Group of 4 out of 10 children - Group of 4 out of 4 girls.
=> 10C4 - 4C4
=> 210 - 1
=> 209
Q3. 20% of A is B, then B% of 20 is same as what?
A. 4% of A
B. 10% of A
C. 20% of A
D. None
ANSWER: A. 4% of A
Solution: It is given that B measures 20% of A
=> So, 20% of A = B or 20/100 * A = B - (1)
B% of 20= B/100 X 20= 2B/10 ---(2)
=> Now, B% of 20
Substituting (1) in (2) we get
2*(2A/10) / 10= 4A/100
Hence, B% of 20 = 4% of A
Q4. With an investment of 45000, X starts a business which is joined by Y after 3 months with 30000. How should they share the profit at the end of the year?
A. 1:3
B. 2:1
C. 1:3
D. 3:1
ANSWER: B. 2:1
Solution: Let us consider the relationships here:
Time and Profit ---------------Direct Relationship ---- More time More profit
Investment & Profit ------Direct Relationship ---- More investment More profit
Ratio of profit = Investment * Time of Investment
= 45000 * 12 : 30000 * 9
= 2:1
Q5. A container has 40L milk. 4L milk is taken out and replaced with water, the process done three times. What is the amount of milk now left?
A. 28L
B. 29L
C. 29.16L
D. 28.4L
ANSWER: C. 29.16L
Solution: In regard to the problem let after n times liquid in the container is x and liquid removed is y
=>Liquid in container= x
=>Liquid removed= y
After one trial, quantity of pure liquid= x- (1-y/x)
After n trials quantity of pure liquid = x - (1 -y/x)n
Therefore, Putting the values ( x = 40L y = 4L N=3) and solving
=> 40- (1-4/40)3
= 29.16L
Q6. The cost price of a particular amount of articles is same as the number of articles. Selling price of the articles comes out to be 20. Over the whole transaction 25% is gained. What is X?
A. 15
B. 18
C. 16
D. 20
ANSWER: C. 16
Solution: According to the question let n be the number of articles.
=> Cost price of n articles = n
=> Selling price of n articles = 20
=> Profit % = 25%
=> Profit % = (SP - CP)/CP X 100
Putting the values in the formula
(20-n)/n x 100 = 25
=> 5n/4 = 20
=> n = 16
Q7. Three coins are tossed. What is the probability of getting at most two tails?
A. 7/8
B. 1/8
C. 2/8
4. 4/8
ANSWER: A. 7/8
Solution: It is given that 3 coins are tossed simultaneously.
=>Total outcomes when one coin is tossed=2
=>Total outcomes when 3 coins are tossed= 2n = 2 X 2 X 2
=8 outcomes
Favourable outcomes: TTH, THT, HTT, THH, THT,HHT,HHH=7
Therefore, Probability= 7/8
Q8. A pump fills a tank in 2 hours. Due to a leak it took 2 2/3 hours to fill the tank. In how much time will the leak drain the entire tank?
A. 6 hours
B. 8 hours
C. 9 hours
D. 10 hours
ANSWER: B. 8 hours
Solution: It is given that tank is filled in 2 hours. Let tank drain out in y hours
=> Part of the tank filled in one hour = 1/2
=> Part emptied in one hour by leak = 1/y
=>Part filled in one hour following leak = 1/ (8/3)
In one hour: 1/2 - 1/7 = 3/8
Therefore, Solving for y, y=8
Q9. For a race a distance of 224 meters can be covered by P in 28 seconds and Q in 32 seconds. By what distance does P defeat Q eventually?
A. 26m
B. 32m
C. 24m
D. 28m
ANSWER: B. 32m
Solution: This is a simple speed time problem. Given conditions:
=>Speed of P= 224/28 = 8m/s
=>Speed of Q=224/32 = 7m/s
=>Difference in time taken = 4 seconds
Therefore, Distance covered by P in that time= 8m/s x 4 seconds = 32 metres
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