UPSC ONLINE ACADEMY

TIME & WORK SET 8

Q.1 A piece of work can be done by 5 men or 9 women in 19 days. In how many days, will 3 men and 6 women complete the same piece of work?

A) 15 days

B) 4 days

C) 6 days

D) 12 days

Ans. A

Five men or 9 women (5 M = 9 W) can do the job = 19 days (Given)
3M = 27/5 W
3 men and 6 women = (27/5 + 6 = 57/5 women) 57/5 women
Time taken by 57/5 women to complete the work = 19 × 9 × 5/57 = 15 days.

Q.2 A contractor undertook a certain work to be done in 80 days and employed 72 men to do it. After 20 days he found that 1/3rd of the work has been finished. How many men should he dismiss in order that the work may be finished on the date agreed upon?
A) 48 men
B) 72 men
C) 24 men
D) 36 men

Ans. C
72 person can finish rd of work in 20 days.
It mean they can complete the remaining job in 40 days.
Now according to the questions
40 × 72 = (72 – x) 60
72 – x = 48
x = 24
To complete the work in 60 days, contractor has to reduce 24 men.

Q.3 The time required by A to complete a piece of work is times the time required by B to complete the same piece of work. If A and B work together, they take 16 days less than the time taken by A alone to complete the piece of work. How many days will B alone take to complete the piece of work?
A) 20 days
B) 40 days
C) 60 days
D) 80 days
Ans. C

Assume B can do the work in ‘d’ days.
So, A needs d days.
A and B together need = days.
It is given – = 16
d = 60 days.

Q.4 ‘C’ can do as much work in 1 day, as A and B together can do in the same period of time. A alone can do the same piece of work in 12 days, whereas B alone can do it in 16 days. If B and C work together, how many days will they take to complete the piece of work?2
A) 3 days
B) 4 days
C) 5 days
D) 3 days
Ans. B
A can do part of the work in 1 day.
B can do part of the work in 1 day.
So, C can do = part of the work in 1 day.
So, B and C can do = in 1 day.
So, it takes = 4 days.

Q.5 Rahul is sailing at a uniform speed when a leak develops in his boat. He uses a bucket to empty water from the boat and reaches the shore in 30 minutes just in time to avoid sinking. The leak fills the boat twice as fast as the Rahul is able to empty it. Had the leak developed 10 minutes earlier how much faster would the Rahul have had to work to reach the shore safely?
A) 20 %
B) 25 %
C) 30 %
D) 35 %
Ans. B
Let r = rate of removing water from the boat
then
2r = rate of water leaking into the boat
let a boat full of water, ready to sink = 1
30/r – 30/2r=1
2(30) – 30 = 2r
60 – 30 = 2r
30 = 2r
r = 15 rate of removing water from the boat
:
Find the rate if leak occurs 10 min earlier (40 min to the shore)
40/r-40/2r=1
2(40) – 40 = 2r
2r = 40
r = 20 rate of removing water from the boat
I guess you could say remove the water; 5/15 = 33% faster

Q.6 A does a work in 90 days, B in 40 days and C in 12 days. They work one after another for a day each, starting with A followed by B and then by C. If the total wages received is Rs. 360 and A, B and C share it in the ratio of the work done, find their respective individual wages.

A) Rs. 40, Rs. 60 and Rs. 260
B) Rs. 36, Rs. 81 and Rs. 243
C) Rs. 42, Rs. 86 and Rs. 232
D) None of these
Ans. B

1/90+1/40+1/12=43/360

43*8/360=344/360

so 16/360 -1/90=1/40

1/40-1/30=1/120

1/120/1/12=1/10

9*1/90:9*1/40:81/10*1/12

4:9:27

4/40*360=36
9/40*360=81
27/40*360=243

Q.7 In one day a man can do twice the amount of work done by a child in a day. It takes 40 days for 50 children working for 8 hours a day to complete the piece of work. If 40 men work for 5 hours a day, how many days will it take them to complete the same piece of work?
A) 40 days
B) 60 days
C) 80 days
D) 10 days
Ans. C

20 men is equivalent to 90 children.
=
= =
d2 = 80 days.

Q.8 In how many ways 19 people can be seated around two round tables with seating capacities of 9 & 10 people.
A) 19!/9!
B) 8!/9!
C) 19C9*8!*9!
D) 2*19C9*8!*9!
Ans. D
Out of two tables , 1 table can be selected in 2 ways.
Out of 19 people , 9 people can be selected in 19C9 ways & 9 people can be arranged around a circular table in 9-1= 8! Ways.
Also, 10 people can be arranged around a circular table in 10-1=9! Ways.
Therefore, Total no. of ways=2*19C9*8!*9!

 

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