Aptitude model placement papers with solution - set 121. Pipes A and B fill a tank in 5 and 6 hours respectively. Pipe C empties the tank in 12 hours, if you open all the three pipes together this tank will be filled in?
A. 3 9/17 hours
B. 4.5 hours
C. 1.25 hours
D. 4 7/17 hoursView Answer / Hide Answer
2. Two trains each of which is 100 m long moving in opposite direction to one another cross each other taking 8 seconds. If speed of one train is twice the speed of other train find the speed of the faster train.
ANSWER: A. 3 9/17 hours
Solution: It is given that Pipe A,B and C work simultaneously.
Pipe A and B are filling the tank and Pipe C is emptying it.
In 1 hour volume of tank filled by Pipe A: 1/5th
In 1 hour volume of tank filled by Pipe B: 1/6th
In 1 hour volume of tank emptied by Pipe C: 1/12th
Working together Pipe A B and C fill x volume of tank.
=>1/x = (1/5)+(1/6)-(1/12)
A. 48 km/hr
B. 30 km/h
C. 60 km/hr
D. 40 km/hrView Answer / Hide Answer
3. A boat with speed 15 km/hr in standing water goes 30 km downstream and returns in a total of 4.5 hours. What is the speed of current?
ANSWER: C. 60 km/hr
Solution: Let the speed of the slower train be x m/sec.
Then speed of faster train becomes: 2x m/sec
Relative speed =x+2x=3x
(100+100)/8 = 3x
x = 25/3 m/sec
=>Speed of faster train= 2x=2*25/3 =50/3 m/sec
Converting into km/hr
A. 4 kmph
B. 6 kmph
C. 5 kmph
D. 8 kmphView Answer / Hide Answer
4. Simple interest at x% for x years will come out to be Rs x on a sum of Rs?
ANSWER: C. 5 kmph
Solution: Speed of the boat in still water: 15 km/hr
Speed of boat downstream: (15+x)km/hr where x is speed of the current.
The boat travels 30 km downstream and then 30 km upstream and takes 9/2 hours.
Total time= Time taken to travel downstream + Time taken to travel upstream
=> 4/5= (30/(15+x))+(30/(15-x))
D. 100xView Answer / Hide Answer
5. Presently a mixture in a tub contains substances A and B in the ratio of 7:5. If 9 litres of this solution is drawn out and B is added to the mixture in certain quantity the resulting mixture becomes 7:9. How much litres of liquid A was kept in the tub initially?
ANSWER: B. 100/x
Solution: Formula for Simple Interest:
SI = Principal*Rate*Time
=> x= Principal*(x/100)*x
=>Principal Amount= 100/x
D. 21 View Answer / Hide Answer
6. logab x logbc x logcb = ?
ANSWER: D. 21
Solution: Currently the mixture is in ratio of A/B: 7:5
=> This means fraction of A in the solution: 7/12
=> Fraction of B in the solvent: 5/12
=>New concentration of A= 7-(7/12)9
=>New concentration of B= 5-(5/12)9+x
=> (7-(7/12)9)/(5-(5/12)9+x) = 7/9
D. ab + bc + caView Answer / Hide Answer
7. Volume of a sphere with radius r is obtained by multiplying its surface area by r and a constant. Find the value of constant:
ANSWER: B. 1
Solution: To solve this question you must remember that:
Logab= logb/loga (logx= log10x)
D. 1View Answer / Hide Answer
8. Find the odd one out:
ANSWER: B. 1/3
Solution: Volume of a sphere: (4/3)* π*r3
Area of a sphere: 4πr2
=>It is mentioned that surface area when multiplied by r and a constant gives Volume and value of constant is to be found.
=> 4πr2*r*k= (4/3)* π*r3
125, 106, 88, 76, 65, 58, 53
D. 76View Answer / Hide Answer
9. A pineapple costs Rs 7 each and a watermelon costs Rs. 5 each. If I spend Rs 38 on total what is the number of pineapple I purchased?
ANSWER: A. 88
Solution: This sequence represents a series in which from the reverse order a prime number is added:
Hence 88 is the answer.
D Data InadequeteView Answer / Hide Answer
ANSWER: C. 4
Answer: The equation for this problem can be made as:
5x + 7y =38
Where x is the number of watermelons and y is the number of pineapples.
Now test for 2, 3 and 4:
For y = 2
5x + 14 =38
x is not an integer
For y = 3
5x = 17
X not an integer
For y =4
X = 2
So 4 pineapples and 2 watermelons can be bought by 38 Rs.