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Most important time and work questions for SBI PO prelims part 1


SBI Clerk and SBI PO Prelims exam are going to be held in the upcoming months. We have already provided you with the PDFs of many topics of Quantitative Aptitude like Simplification/Approximation, Number Series,datainterpretation.important Arithmetic questions to prepare for SBI Clerk and PO Pre exam. Practicing these questions will help you to know about the level of the questions. To increase your speed and accuracy, enhance your calculations.

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START QUIZ

1. A tyre has two punctures. The first puncture alone would have made the tyre flat in 9 minutes and the second alone would have done it in 6 minutes. If air leaks out at a constant rate, how long does it take both the punctures together to make it flat? 
a) 1 
b) 3 
c) 3
d) 4 
e) None of these

2.Two pipes A and B can fill a cistern in 15 hours and 10 hoursrespectively. A tap C can empty the full cistern in 30 hours. All the 
three taps were open for 2 hours, when it was remembered that the emptying tap had been left open. It was then closed. How many hours more would it take for the cistern to be filled?
a) 30 min. 
b) 1.2 hours 
c) 24 min. 
d) 35 min. 
e) None of these

3.45 men can complete a work in 16 days. Six days after they started working. 30 more men joined them. How many days will they now take to complete the remaining work? 
a) 18 days 
b) 12 days 
c) 9 days 
d) 6 days 
e) None of these

4.Pipe A basically used as inlet pipe and pipe B is used as outlet pipe. Pipes A and B both are opened simultaneously, all the time. When pipe A fills the tank and B empty the tank, it will take double the time than when both the pipes fill the tank. When pipe B is used for filling the tank, its efficiency remains constant. What is the ratio of efficiency of pipe A and pipe B respectively? 
a) 3 : 1 
b) 5 : 2 
c) 1 : 3 
d) 3 : 2 
e) None of these

5.A is twice as good a workman as B and together they finish a piece of work in 18 days. In how many days will A alone finish the work? 
a) 72 days 
b) 30 days
c) 27 days 
d) 32 days 
e) None of these

6)A and B undertake to do a piece of work for Rs.600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they finish it in 3 days. Find the share of each. 
a) Rs.80 
b) Rs.75 
c) Rs.90 
d) Rs.82 
e) None of these

7)Tap A can fill the empty tank in 12 hours, but due to a leak in the bottom it is filled in 15 hours, if the tank is full and then tap A is 
closed then in how many hours the leak can empty it? 
a) 45 hours 
b) 48 hours 
c) 52 hours 
d) 60 hours 
e) None of these

8)4 men and 2 boys can finish a piece of work in 5 days. 3 women and 4 boys can finish the same work in 5 days. Also 2 men and 3 women can finish the same work in 5 days. In how many days 1 man, 1 woman and one boy can finish the work, at their double efficiency?
a) 4 
b) 4 
c) 3 
d) Data inadequate 
e) None of these

9) B and C are equally efficient, but the efficiency of A is half of each B and C. A and B started a work and 3 days later C joined 
them. If A alone can do the work in 14 days, then in how many more days the work will be completed? 
a) 1 
b) 2 
c) 3 
d) 4.5 
e) None of these

10) A and B together can complete a piece of work in 4 days. If A alone can complete the same work in 12 days, in how many days can  B Blone complete that work? 
a) 6 days 
b) 12 
c) 8 days 
d) 9 days 
e) None of these

11) A contractor undertook a work to complete in 60 days. But just after 20 days he observed that only th of the project work had been completed. To complete the work in time (i.e., in rest days) minimum how many workers he had to increase, if there were initially 75 workers were deployed for the task? 
a) 25 
b) 50 
c) 75 
d) Data inadequate 
e) None of these

12) If 2 men or 3 women or 4 boys can do a piece of work in 52 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in : 
a) 48 days 
b) 36 days 
c) 45 days 
d) Data inadequate 
e) None of these

13) A contractor undertook to complete the work in 40 days and he deployed 20 men for his work. 8 days before the scheduled time he realized that 1/3rd of the work was still to be done. How many more men were required to complete the work in stipulated time? 
a) 16
b) 15 
c) 20 
d) 25 
e) None of these

14)A and B undertook a work for Rs.350. A got Rs.150 more than that of B, when they worked together. B takes 9 days more than A, when they work individually. In how many days A and B working together can do the whole work: 
a) 5 
b) 4 
c) 4
d) 5 
e) None of these

15) When A, B and C are deployed for a task, A and B together do 70% of the work and B and C together do 50% of the work. Who is most efficient? 
a) a 
b) b
c) c 
d) Data inadequate 
e) None of these


SOLUTIONS

1. Option C
1 minute’s work of both the punctures = [1/9 + 1/6]= 5/18
So, both the punctures will make the tyre flat in 18/5=3 3/5 min.

2. Option C
Time taken by pipes A and B to fill the whole tank = 100/16.66 =6 hrs
Capacity filled in 2 hours by pipes A, B and C = 2 × 13.33 
= 6 hours = 26.66% 
Remaining capacity = 73.33% 
This remaining capacity can be filled by A and B 73.33/16.66= 4 2/5
So, the total time required = 2 + 4 2/5 = 6 hours 24 minutes
Thus, in this case 24 minutes extra are required.

3.Option E
(45 × 16) men can complete the work in 1 day. 
So, 1 man’s 1day’s work =1/720
45 men’s 6 day’s work = [1/16*6]=3/8
Remaining work = [1 3/8]=5/8

4.Option A
Efficiency when both pipes used to fill = A + B 
And efficiency when pipe A is used to fill and pipe B is used to empty 
the tank = A B
So, A+B/AB =2/1
A/B=3/1
= Thus, the ratio of efficiency of pipe A and B = 3 : 1

5.Option C
(A’s 1 day’s work) : (B’s 1 day’s work) = 2 : 1 
(A + B)’s 1 day’s work = 1/18
Divide in the ratio 2 : 1
So, A’s 1 day’s work = [1/18 * 2/3]=1/27 
Hence, A alone can finish the work in 27 days.

6.Option B
C’s 1 day’s work = 1/3 [1/6+1/8]=1/24
A : B : C = Ratio of their 1 day’s work =1/6 :1/8 :1/24 = 4 : 3 : 1
A’s share Rs. [600*4/8]= Rs.300, 
B’s share = Rs.[600*3/8]= 225Rs
C’s share = Rs.[600 (300+225)]= Rs.75

7. Option D
Efficiency of A = 8.33% Effective 
efficiency = 6.66%, when there is leakage 
So, efficiency of leakage = 1.66% = (8.33 6.66) 
It means due to leakage a full tank will be empty in 60 hours.

8.Option E
Efficiency of 4 men and 2 boys = 20% 
Efficiency of 3women and 4 boys = 20%
Efficiency of 2 men and 3 women = 20%
So, Efficiency of 6 men, 6 women and 6 boys = 60% 
So, efficiency of 1 man, 1 woman and 1 boy = 10% 
Now, since they will work at double their efficiency 
Efficiency of 1 man, 1 woman and 1 boy= 20% 
Required number of days = 5

9.Option A
Number of days taken by A to complete work alone = 14 days 
Number of days taken by B to complete work alone = 7 days 
Number of days taken by C to complete work alone = 7 days 
One day’s work of A and B = 1/14+1/7 =3/14
And one day’s work of A, B and C = 1/14+1/7 +1/7 =5/14
3 day’s work of A and B = 3 × 3/14= 9/14
Remaining work = 5/14 [1 9/14]
This remaining work will be done by A, B and C = 5/14 ÷5/14=
1 day

10.Option A
(A + B)’s 1 day’s work = 1/4, 
As 1 day’s work = 1/12
B’s 1 day’s work=[1/4 1/12]=1/6
Hence, B alone can complete the work in 6 days.

11.Option C
Work done =1/5
Remaining work = 4/5
4 (20 × 75) = 40 × x x = 150 
Therefore 75 men should be increased.

12. Option E
Work done by 2 men = 3 women = 4 boys 
1 man = 2 boys 
1 women = 4/3boys 
Boys × days = 4 × 52 (boys days) 
Again 1 man + 1 woman + 1 boy = 2 + 4/3+ 1 =13/3 boys

13. Option C
Work done = 2/3
Remaining work = 1/3 ,
which is half of 2/3
1/20× (20 × 32) = 8 × x 
x = 40 men 
Therefore, 20 more men were required.

14.Option B
A’s share = Rs.250 
B’s share = Rs.100 
It means the ratio of efficiency of A : B = 250 : 100 = 5 : 2 
Ratio of days taken by A and B = 2x : 5x 
Now, 5x 2x = 9 x = 3 
Number of days taken by A = 6 (efficiency = 16.66%) 
Number of days taken by B = 15 (efficiency = 6.66%) 
Therefore number of days taken by A and B, working together =
=1000/23.33 =300/70= 4 2/7 days

15. Option A
A + B = 70%
B + C = 50%
{A + B + B + C (A + B + C) = B}
70 + 50 100 = 20% 
B = 20% 
A = 50% 
C = 30% 
Hence, A is most efficient