Test: Arun Sharma Based Level 1: Time & Work


15 Questions MCQ Test Quantitative Aptitude (Quant) | Test: Arun Sharma Based Level 1: Time & Work


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QUESTION: 1

Directions for Question: A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

Q. How many minutes will it take to fill the tank if all the 23 pipes are opened at the same time?

Solution:

It is given that pipes of set x can fill 70% of the tank in 7 min.

  • set x = 70/100 th in 7 min  

It means that, 1/10 th tank is filled in 1 min.

Similarly,  

It is given that pipes of set y can fill 3/8 th of the tank in 3 min.

So, we write as,

  • set y = 3/8 th of tank in 3 min  

It means that, 1/8 th tank is filled in 1 min.

And,  pipes of the set z can empty 5/10 th  of the tank in 10 min.

  • set z = 5/10 th  in 10 min  

Therefore, 1/20 th  tank is emptied in 1 min.

So,  we consider all three sets for one minute. Then,

1/10 + 1/8 - 1/20 = 7/40 th tank is filled in one minute.

Thus, the time required to fill the tank completely = 40/7 minutes

QUESTION: 2

Directions for Question : A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

Q. If only half the pipes of set X are closed and only half the pipes of set Y are open and all other pipes are open, how long will it take to fill 49% of the tank?

Solution:

►Set X will do 5% per minute and Set Y will do 6.25% per minute, while set Z will do 5% per minute (negative work).

►Hence, Net work will be 6.25% per minute. To fill 49% it will take slightly less than eight minutes and the value will be a fraction.

►None of the first three options matches this requirement. 

QUESTION: 3

Directions for Question: A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

Q. If 4 pipes are closed in set Z, and all others remain open, how long will it take to fill the tank?

Solution:

►If 4 of the taps of set Z are closed, the net work done by Set Z would be -2.5% while the work done by Sets X and Y would remain 10% and 12.5% respectively.

►Thus, the total work per minute would be 20% and hence the tank would take 5 minutes to fill up.

QUESTION: 4

Directions for Question: A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

Q. If the tank is half full and set X and set Y are closed, how many minutes will it take for set Z to empty the tank if alternate taps of set Z are closed.

Solution:

►Again if we close 4 taps of set Z, the rate of emptying by set Z would be 2.5% per minute.

►A half filled tank would contain 50% of the capacity and hence would take 50 / 2.5 = 20 minutes to empty.

QUESTION: 5

Directions for Question: A set of 10 pipes (set X) can fill 70% of a tank in 7 minutes. Another set of 5 pipes (set Y) fills 3/8 of the tank in 3 minutes. A third set of 8 pipes (set Z) can empty 5/10 of the tank in 10 minutes.

Q. If one pipe is added for set X and set Y and set Z ' s capacity is increased by 20% of its original value and all the taps are opened at 2.58 p.m., then at what time does the tank gets filled? (If if is initially empty).

Solution:

►The rate per minute with the given changes (in percentage terms) would be :

►Set X = 11%, Set Y = 15% and Set Z = -6%.

►Hence, the net rate = 11 + 15 - 6 = 20%, per minute and it would take 5 minutes for the tank to fill. If all pipes are opened at 2:58, the tank would get filled at 3:03.

QUESTION: 6

Ajit can do as much work in 2 days as Baljit can do in 3 days and Baljit can do as much in 4 days as Diljit in 5 days. A piece of work takes 20 days if all work together. How long would Baljit take to do all the work by himself?

Solution:

►Let Ajit's rate of work be 100/2 = 50 work units per day.

►Baljit would do 100/3 = 33.33 work units per day and Diljit does 133.33/5 = 26.66 units of work per day.

►Their 1 day work = 50 + 33.33 + 26.66 = 110 units of work per day.

►In 20 days, the total work done would be 2200 units of work and hence for Baljit to do it alone it would take : 2200 / 33.33 = 66 days to complete the same work.

QUESTION: 7

Mini and Vinay are quiz masters preparing for a quiz. In x  minutes, Mini makes y questions more than Vinay. If it were possible to reduce the time needed by each to make a question by two minutes, then in x minutes Mini would make 2y questions more than Vinay. How many questions does Mini make in x minutes?

Solution:

Solve by trial and error by putting values for x and y in the options.

QUESTION: 8

A pipe can fill a tank in x hours and another can empty it in y hours. If the tank is 1 / 3rd full then the number of hours in which they will together fill it in is

Solution:

►To solve this question first assume the values of x and y (such that x < y).

►If you take x as 10 hours and y as 15 hours, you will get a net work of 3.33% per hour.

►At this rate it will take 20 hours to fill the tank from one third full. Using this condition try to put these values of x and y into the options to check the values.

►For instance option (a) gives the value as 3 x 10 x 15 /10 = 45 which is not equal to 20.

QUESTION: 9

A finishes 6 / 7th of the work in 2z hours, B works twice as fast and finishes the remaining work. For how long did B work?

Solution:

Since A finishes 6 / 7th of the work in 2z hours.
B would finish 12 / 7 of the work in 2z hours.
Thus, to do 1/7th of the work (which represents the remaining work), B would require
     ► 2z /12 = z / 6 hours.

QUESTION: 10

Three diggers dug a ditch of 324m deep in six days working simultaneously. During one shift, the third digger digs as many metres more than the second as the second digs more than the first. The third digger's work in 10 days is equal to the first digger's work in 14 days. How many metres does the first digger dig per shift?

Solution:

►The per day digging of all three combined is 54 metres. Hence, their average should be 18.

►This means that the first should be 18 - x, the second, 18 & the third 18 + x.

►The required conditions are met if we take the values as 15, 18 and 21 metres for the first, second and third diggers, respectively. 

QUESTION: 11

Direction for Question: Read the passage below and solve the questions based on it.

A person can dig a trench 40 metres in depth in 4 days working 8 hrs a day. However, after every day he finds that one-fifth of the depth got filled up with mud again.

Q. In how many days can he actually dig a trench if it is of 30 metres in depth?

Solution:

►Efficiency = 40 / 4 = 10m / day

►The work in each day if for 8 hours, so efficiency (in hrs) = 40 / 32 = 1.25m / hrs

►After a day 2m is again filled with mud.

►So in a day he can dig only 8 meters
So on the 5th day

QUESTION: 12

Direction for Question: Read the passage below and solve the questions based on it.
A person can dig a trench 40 metres in depth in 4 days working 8 hrs a day. However, after every day he finds that one-fifth of the depth got filled up with mud again.

Q. What was the depth of the trench at the beginning of the fourth day?

Solution:

First day — 8
Second day — 18 x (4 / 5) = 14 .4
Third day — 14.4 + 10 = 24.4 x (4 / 5) = 19.52

QUESTION: 13

Direction for Question: Refer to the data below and answer the questions that follow: 

Anoop was writing the reading comprehension sections in the SIP entrance examinations. There were four passages of exactly equal length in terms of number of words and the four passages had 5, 8, 8 and 6 questions following each of them, respectively. It is known that Anoop can answer exactly 12 questions in the time he takes to read any one of the the four passages. Assume that his rate of reading and answering questions remains the same throughout the section.

Q. Anoop took 13 min more to finish the first three passages than the time he took to finish the last passage. Assuming that Anoop answered all the questions in each passage, what percentage of the total time did he spent on the first passage?

Solution:

►Let us assume that time to read one passage = x

►So, according to the question, 3x + 21( x / 12) - 13 ⇒ x = 4

►Therefore, total time taken for answering all questions = 4 x 4 + (4 x 27 / 12) = 25 min

►Time spent on first passage = 4 + (4 x 5 / 12) = 17 / 3 min

►Required percentage = 22 .6%

QUESTION: 14

Direction for Question: Refer to the data below and answer the questions that follow: 

Anoop was writing the reading comprehension sections in the SIP entrance examinations. There were four passages of exactly equal length in terms of number of words and the four passages had 5, 8, 8 and 6 questions following each of them, respectively. It is known that Anoop can answer exactly 12 questions in the time he takes to read any one of the the four passages. Assume that his rate of reading and answering questions remains the same throughout the section.

Q. By what per cent should Anoop increase his reading speed if he has to cut down on his total time spent on the section by 20%? Assume that the time spent on answering the questions is constant and as given in the directions.

Solution:

►As we have found in the previous question that total time spent = 25 min

►If total time spent is cut down by 20%, then time = 20 min

►Now, let us assume increased reading speed = x

►So, 20 = 4 x + (4 x 27 / 12) ⇒ x =11 / 4 = Multiplication.

►Hence, percentage increase = 45.45%

QUESTION: 15

P, Q and R each complete a certain work in 16, 20 and 30 days, respectively. The three of them start the work together. P leaves after 4 days;  Q leaves 4 days before the work is finished? How long did the work last?

Solution:

P—16—15
Q—20—12
R—30—8
LCM = 240
 ► 35 x 4 + 8 x 4 = 140 + 32 = 172
 ► 240 - 172 = 68
 ► 68 / 20 = 3.4
Total time = 4 + 4 + 3.4 = 11.4 days