Below are three sample time based aptitude problems. This is one of the most occurring sections considering any standard placement paper of leading companies. Hence it is very important to be well prepared to solve these kinds of questions.
Question 1
Construction of a water tank was completed recently in La Celeste Complex. It was fitted with two pipes – one a BIG pipe and another a SMALL pipe. BIG pipe when used for filling the water tank it takes 8 hours. The tank is filled fully by SMALL pipe in 10 hours. The contractors wanted to find out how long it will take if SMALL pipe is switched on for an hour and BIG pipe is switched on for the next hour. If this process is repeated how long it will take for the tank to be filled in completely.
a) 12 hours b)9 hours c)5 hours d)8 hours
Answer : b) 9 hours.
Solution :
SMALL pipe (S) can fill in one hour 1/10 of the water tank.
BIG pipe (B) can fill in one hour 1/8 of the water tank.
So in two hours (first S Pipe is open for the first hour and then B pipe is open for the second hour) tank would be filled by = 1/8 + 1/10 = 18/80 = 9/40 of the tank.
So in 4 times this i.e. 8 hours both the pipes will fill = 36/40 of the tank
Balance = 4/40 = 1/10.
So when for the 9th hour S pipe runs the tank will be full.
That means it takes totally 9 hours for the two pipes to fill in this order.
Question 2
There are two types of pipes fitted for a water tank kept in the 15th floor top of the new building constructed by Kaizen Constructions recently in Maharanipet, Hyderabad. The motor is kept on the ground near the corporation water sump from which the water is pumped up. Reddy Pipe takes 50 minutes to fill the tank. Rao Pipe takes 100 minutes to fill the tank.
Both pipes were started at 10.30 am. Rao pipe was closed after some time. Reddy pipe continued to fill water to the tank and the tank got filled at 11.10 am. At what time the Rao pipe was closed?
a)10.40 am b) 10.50 am c) 11.00 am d) cannot be determined.
Answer : b) 10.50 am
Solution :
Reddy pipe can fill in one minute 1/50 of the tank
Rao pipe can fill in one minute 1/100 of the tank.
In one minute when both the pipes run they will fill
1/50 + 1/100 = 3/100 of the tank.
Minutes Taken Tank Filled By Both The Pipes 1 3/100 ? Full
If both the pipes run they will take 100/3 = 33 1/3 minutes to fill the Full tank.
But since Rao pipe was closed after X minutes it has taken 40 minutes for the other pipe to complete filling the tank.
Minutes Taken Tank Filled By Reddy's Pipe 1 1/50 40 ?
In 40 minutes Reddy pipe would had fill 1/50 x 40 = 4/5 of the tank.
That means 1 - 4/5 = 1/5 of the tank should had been filled by Rao pipe.
Minutes Taken Tank Filled By Rao's Pipe 1 1/100 ? 1/5
Rao pipe has worked for 1/5 x 100/1 = 20 minutes
So Rao pipe was closed 20 minutes after 10.30 i.e till 10.50 am.
Question 3
Sumanth Constructions took up fitting up of two taps called Apple and Micro and these fill the tank in 24 minutes and 40 minutes respectively. Apple pipe runs for one minute and closed. Then for the next one minute Micro pipe runs and closed. This process is repeated for upto 12th minute end. Then the balance volume of water to be filled in the tank to make it fill – in terms of percentage is:
a)60% b)50% c)33 1/3% d) 45%
Answer : a)60%
Solution :
Apple tap will fill 1/24 of the tank in one minute.
Micro tap will fill 1/40 of the tank in one minute.
According to the problem
Apple pipe runs for one minute and then Micro pipe runs for next one minute.
So in 2 minutes they will together as above = (1/24 + 1/40) = 1/15
So in six times the above process or in totally 12 minutes they will fill 1/15 x 6 = 6/15 = 2/5 th of the tank
Balance to be filled in = 1 - 2/5 = 3/5
Balance to be filled in terms of percentage = 3/5 x 100 % = 60%