# Crack IBPS PO : Miscellaneous – Aptitude Day 65

D.1-10) Study the following and answer the questions:

Q.1) Ashok can do some work in 10 days, Mohan in 20 days and Vijay can do it in 25 days. They start working in turns with Ashok starting to work on the first day, Mohan on second day and Vijay on the third day and so on. They work in the way for 12 days. After this, Vijay is replaced by Sohan who can complete the work in 20 days by himself. Find the time taken to complete 96% of the work.

a) 18 days

b) 15 days

c) 12 days

d) 20 days

e) None of these

b)

Ashok does 10% work per day, Mohan 5% and vijay 4%

In three days, they complete 19% work.

Thus in 12 days, they are able to complete 76% work.

Remaining work = 24%.

Sohan can complete the work in 20 days.

Thus he does 5% work daily.

Ashok, Mohan and Sohan, working alternatively, complete 20% work in three days.

Time taken to complete 96% of the work = 12 +3 = 15 days.

Q.2) 24 workers can build a wall in 10 days by working 8 hours a day. They started the work but after 4 days 8 workers left. How many hours a day should the remaining workers work to complete it on time?

a) 14 hours

b) 13 hours

c) 15 hours

d) 12 hours

e) None of these

d)

Work done by 24 men in 10 days working 8 hours a day = 24×10×8 = 1920

Hence total work can be given as =1920

When 8 workers leave after 4 days, remaining workers = 24-8 =16

Let ‘h’ be the number of hours the 16 workers work to complete the wall in remaining 6 days.

Now, total work can be given as: work by 24 workers in 4 days + work by 16 workers in 6 days = 24×4×8 +16×6×h

1920 = 24×4×8 + 16×6 ×h

1920 = 768+ 96h

H =12

Q.3) 16 men is supposed to do a work in 54 days. After 30 days 4 more men is employed and the work is completed in 4 days before the scheduled time.  How many days it have been delayed if 4 more men were not employed?

a) 1 day

b) 2 day

c) 3 day

d) 4 day

e) None of these

a)

16×30 + 20×20 = total work = 16×T (T is the number of days when 4 more men are not employed)
we get T = 55, so work will be delayed by 1 day

Q.4) one pipe can empty a tank 5 times as fast as another pipe. If both the pipes together can empty the tank in 18 minutes, then the slower pipe alone will empty the tank in how many minutes?

a) 102 minutes

b) 114 minutes

c) 126 minutes

d) 132 minutes

e) None of these

e)

Let the slower pipe alone empty the tank in = x min

The faster pipe can empty the tank in = x min

Part emptied by the slower pipe in 1 min =1/x

Part emptied by the faster pipe in 1 min =1/(x/5)=5/x

Part emptied by both the pipes together in 1 min 1/x+5/x

Given that both the pipes together can empty the tank in 18 min

Part emptied by both the pipes together in 1 min =1/18

For one min :1/x+5/x=1/18

=6/x=1/18

So, x = 6×18 = 108

Time taken by slower pipe to empty the tank = 108 min

Q.5) X and Y can complete a task in 20 days, when working together. After X and Y have been working together for 10 days, Y is called away and X, all by himself completes the task in the next 15 days. Had X been working alone, the number of days taken by him to complete the task would have been

a) 40 days

b) 60 days

c) 30 days

d) 32 days

e) None of these

c)

Both X and Y can do work in 20 days.

So work done in 1 day =1/20 thwork

In 10 days, work done =1/20×10= 1/2 work

In 15 days, work done by X alone =1/2 work

In 1 day , X can do =1/30 thofthework

So, tdays X will take to complete whole work = 30 days.

Q.6) Two pipes A and B can fill a cistern in 10 hours and 15 hours respectively. C tap can empty the full cistern in 20 hours. All the three taps were open for 3 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) 4 hours 24 minutes

b) 3 hours 48 minutes

c) 3 hours 53 minutes

d) 3 hours 54 minutes

e) None of these

d)

Let the capacity of the tank be 60 litres (LCM of 10 and 15)

Speed at which tank is filled by Tank A = 6 litres/hour

Speed at which tank is filled by Tank B = 4 litres/hour

Speed at which tank is emptied by Tank C = 3 litres/hour

Time taken by pipes A and B to fill the Whole tank =60/10=6 hours

Tank filled in 3 hours by pipes A, B and C = 3 ×(6+4-3) = 21 litres

Remaining capacity to be filled = 60-21 = 39 litres

The remaining capacity can be filled by A and B =39/10=3.9 hours

Thus, in this case 3.9 hours or 3 hours 54 minutes are required more.

Q.7) A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A left after some days and then B completed the remaining part of the work in 23 days. The number of days after worker A left the work was?

a) 9 days

b) 10 days

c) 11 days

d) 12 days

e) None of these

a)

A can do 1/45 th work in 1 day.

B can do 1/40 th work in 1 day.

Together they can do 17/360 th work in a day.

Number of days required by them together =360/17

In 23 days, B would have done 23/40×100=57.5% of the work

So, A and B would have worked together for 42.5% of the work.

Therefore, number of days after A left =360/17×42.5/100=9 days.

Q.8) There are 7 people in an organisation comprise of 2 boys and 5 men, each boys works at one-third the rate of each men. What is the ratio of time taken when all the 7 people are working together to the time taken when only 5 men are working together?

a) 15 : 19

b) 17 : 19

c) 15 : 17

d) 17 : 21

e) None of these

c)

Let a man takes x days so boy will take 3x days, work done by a men in one day is 1/x and by boy is 1/3x. so work done

by all in one day =5/x+2/3x=17/3x

Total number of days to finish work is 3x/17

Number of days required by 5 men to finish the work is x/5days.

Required ratio 3x/17  : x/5 = 15 : 17

Q.9) Three pipes A, B and C can fill a certain cistern in 20, 24 and 30 minutes respectively. While another pipe D empties it at rate of 3.2 gallons/minute. If the cistern gets filled completely in 10 minutes when all pipes are opened together, then find cistern’s capacity (in gallons)?

a) 134 gallons

b) 128 gallons

c) 124 gallons

d) 120 gallons

e) None of these

b)

Let total work be 1.

Work of all four pipes together =1/10

Work of pipeA, BandCis 1/20,1/24 and 1/30respectively

Work of pipe D alone =1/10-(1/20+1/24+1/30)=(1/10)-(1/8)= -1/40 (here negative sign means emptying).

Now, volume emptied during 1/40 work = 3.2 gallons

Thus, capacity of cistern = volume emptied in 1 work = 40×3.2 = 128 gallons

Q.10) Raghav started a work and left it after 7 days. The remaining work is completed by Shree. So, the work gets completed in 18 days. Shree can alone finish the work in 14 days. Find the number of days in which Raghav can alone finish the work?

a) 24 1/2 days

b) 32 1/2 days

c) 22 1/2 days

d) 26 1/2 days

e) None of these

a)

Let Raghav can alone complete the work in x days

Work done by Raghav in 7 days =7/x of the complete work

Work left =1-7/x=(x-7)/x

1/14of the work is done by shree in 1 day

(x-7)/xof the work is done by shree in 1 day

18 =14×(x-7)/x

18x = 14x-98

4x = 98

X  = 24 1/2

So, Raghav canal one complete the work in 24 1/2 days.