QUESTIONS ON TIME & WORK (PART-III)

QUERY 21

X and Y can do a piece of work in 36 days. They work together for 24 days and then X left. Y finishes the remaining work in 16 days. In how many days X alone can finish the work?

A) 144 days
B) 140 days
C) 152 days
D) 414 days

MAHA GUPTA
(X + Y)’s 1 day work = 1/36
Therefore work finished by them working together in 24 days = (1/36)24 = 2/3
So, the remaining work = 1 – 2/3 = 1/3

But this remaining work, i.e. 1/3 is finished by Y alone in 16 days
Hence his 1 day work = (1/3)/16 = 1/48

Hence X’s 1 day work = ( X + Y)’s 1 day work – Y’s 1 day work = 1/36 – 1/48 = 1/144
So, the time to be taken by X if he alone does whole of the work = 144 days (option ‘A’)

QUERY 22

6 men complete a piece of work in 12 days, 8 women in 8 days and 18 children in 10 days. IF (12w + 4m + 20c) work for 2 days, then if only men were to complete the remaining work in 1 day, how many men would be required?

A) 72 men
B) 27 men
C) 21 men
D) 24 men

MAHA GUPTA
1 man’s 1 day work=1/(6*12) = 1/72
1 woman’s 1 day work = 1/(8*8) = 1/64
1 child’s 1 day work = 1/(18*10) = 1/180

But 12 women, 4 men and 20 children work together for 2 days; so their 2 day work = 2[(12/64) + (4/72) + (20/180)] = 17/24

Therefore the remaining work = 1 – 17/24 = 7/24

Now this remaining work has be done by men only in 1 day
But 1 man’s 1 day work = 1/72
So number of men needed to do 7/24 of work = 72*(7/24) = 21 men (option ‘C’)

QUERY 23

There was a leakage in the container of the refined oil. If 11 kg oil is leaked out per day then it would have lasted for 50 days. If the leakage was 15 kg per day then it would have lasted for only 45 days. How many days would the oil have lasted, if there was no leakage and it was completely used for eating purpose?

A) 72 days
B) 27 days
C) 30 days
D) 55 days

MAHA GUPTA
Let the oil used for eating in a day = x kg

CASE-I
The quantity used in total in 50 days = 50x kg
Quantity wasted = 11*50 = 550 kg
Therefore total oil in the container = (50x + 550) kg

CASE-II
The quantity used in total in 45 days = 45x kg
Quantity wasted = 15*45 = 675 kg
Therefore total oil in the container = (45x + 675) kg

So, obviously 50x + 550 = 45x + 675
=> x (Consumption of one day)= 25

Total quantity of oil in the tanker = 50x + 550 = 50*25 + 550 = 1800 kg

Hence number of days the oil would have lasted, if there was no leakage = QUANTITY/CONSUMPTION = 1800/25 = 72 (option ‘A’)

QUERY 24

A do as much as work in 16 hr as B do in 24 hr. C can do same work in 32 hr. If together can do in 24 hr. Find C’s hours when he works alone.

A) 96 hours
B) 104 hours
C) 100 hours
D) 80 hours

MAHA GUPTA
Let the work according to the ratio given of A, B and C = 1
Now Work in 1 hour of each according to the ratio
A = 1/16; B = 1/24; C = 1/32
Therefore (A+B+C)’s 1 hour work = 1/16 + 1/24 + 1/32 = 13/96
So total time taken by all of them working together for that 1 work = 96/13 hours

Work finished by them in 96/13 hours = 1
Hence work finished by them in 24 hours = (13/96)24 = 13/4
So actual amount of work is 13/4

Time to be taken by C to do 1 work = 32 hours
Therefore time to be taken by him to do 13/4 work = 32(13/4) 104 hours. (option ‘B’)

QUERY 25

Running at the same constant rate, 6 identical machines can produce a total of 270 bottles per minute. At this rate, how many bottles could 10 such machines produce in 4 minutes?

A) 648
B) 1800
C) 2700
D) 10800

MAHA GUPTA
6 machines can produce number of bottles in 4 minutes = 270*4 = 1080
10 machines can produce number of bottles in 4 minutes = (1080/6)*10 = 1800 (option ‘B’)

QUERY 26

8 men and 10 boys do a work in the same days as 4 men and 16 boys do. 1 man and 3 boys start a work to finish it in 40 days. After 18 days, 9/20th part of the work had been finished. How many boys should be increased to make the work complete in exact time?

A) 0
B) 2
C) 3
D) 9

MAHA GUPTA
Time taken by 1 man and 3 boys to finish 9/20 of work = 18 days

Therefore time to be required by them to finish 1 work i.e. total work = 18(20/9) = 40 days

But there schedule time to finish the whole work also is 40 days
So no additional force is required to finish the work in time. Hence the answer is zero. (option ‘A’)

QUERY 27

If 1 man or 2 women or 3 boys can complete a piece of work in 88 days, then 1 man, 1 woman and 1 boy together will complete it in how many days?

A) 88 days
B) 68 days
C) 48 days
D) 50 days

MAHA GUPTA
Let’s do this sum considering men only
Given 2 women = 1 man; means 1 woman = 1/2 man
And 3 boys = 1 man; means 1 boy = 1/3 man

Therefore 1 man + 1 woman + 1 boy = 1 man + 1/2 man + 1/3 man = 11/6 men

Now time taken by 1 man to complete the work = 88 days
Therefore time to be taken by 11/6 men = 88/(11/6) = 48 days (option ‘C’)

QUERY 28

A’s efficiency is half of B. And C can only do half of A and B together. If C can do whole of the work in 20 days In how many days all working together will finish the same work?

Â) 5²⁄₃ days
B) 6²⁄₃ days
C) 6 days
D) 7 days

MAHA GUPTA
As C’s capacity is half of (A + B), and he alone can finish the work in 20 days
Therefore time to be taken by A and B together to finish the work = 20/2 = 10 days

Now (A + B)’s 1 day work = 1/10
And C’s 1 day work = 1/20

So 1 day work of A + B + C working together = 1/10 + 1/20 = 3/20
Hence number of days taken by all working together = 20/3 = 6²⁄₃ days (option ‘B’)

QUERY 29

A, B and C can do a piece of work in 30, 40, 60 days respectively. A works for whole time. B and C work in alternate days with A. Then how many days the work lasts?

A) 18³⁄₇ days
B) 19 days
C) 19¹⁄₂ days
D) 20 days

MAHA GUPTA
A work daily and B and C on alternate days with A; means the cycle of doing work goes for every set of 2 days. So we need to find here work finished in 2 days.

Now (A + B + C)’s 2 day work = A’s 2 day work + B’s 1 day work + C’s 1 day work
= (1/30)2 + 1/40 + 1/60 = 13/120

It’s obvious to understand that C may not be working on the second day of the last cycle; so let’s find out how much work is finished in complete cycles of doing work

Obviously they will be 120/13 = 9 cycles of 2 days each

Now the work finished in 1 cycle = 13/120
So, work finished in 9 cycles = (13/120)9 = 117/120

Remaining work = 1 – 117/120 = 3/120 = 1/40

Now (A + B)’s 1 day work = 1/30 + 1/40 = 7/120
We see that 1/40 is smaller than 7/120; means C won’t have to work after the last completed cycle

Now time to finish 7/120 of work = 1 day
Thus time to finish 1/40 of work = (120/7)*(1/40) = 3/7 day

Time taken earlier 9 cycles of 2 days each i.e. 18 days

Therefore the total number of days in which the work will last = 18³⁄₇) days (option ‘A’)

QUERY 30

A completes ⁷⁄₁₀ of work in 15 days , then he completes the remaining work with the help of B in 4 days. The time required for A and B together to complete the entire work is?

A) 10²⁄₃ days
B) 12²⁄₃ days
C) 13¹⁄₃ days
D) 13²⁄₃ days

MAHA GUPTA
Work to be done by both in 4 days = 1 – 7/10 = 3/10

Now, Time taken by Both A and B to finish 3/10 of work = 4 days
Therefore time to be taken by both to finish whole i.e. 1 work = 4(10/3) = 40/3 =  13¹⁄₃ days (option ‘C’)