QUESTIONS ON TIME AND WORK (PART-I)

QUERY 1

A man and a boy complete a work together in 24 days. If for the last 6 days man alone does the work then it is completed in 26 days. How long the boy will take to complete the work alone?

A) 27 days
B) 32 days
C) 72 days
D) 30 days

JAYANTCHARAN CHARAN
After the boy has left the work the man alone does the work for 6 days to finish it means takes 2 more days to finish the work (26 – 24). So the boy did work for 20 days (26 – 6)
.
When the man and the boy work together the whole work finishes in 24 days,
so the work finished in 20 days = 20/24 = 5/6
Therefore the remaining work = 1 – 5/6 = 1/6

The man does finishes this remaining work in 6 days, so he alone can complete the whole work in 6 x 6 = 36 days
So man’s one day work = 1/36
and work to be finished in 1 day = 1/24
Therefore boy’s one day work = 1/24 – 1/36 = 1/72
Hence time to be taken by the boy alone to finish the work = 72 days (option ‘C’)

QUERY 2

3 men and 4 women can do a work in 16 days but 4 men and 3 women can do the same work in 12 days; then 2 men and 5 women can do the same work in ?

A) 6 days
B) 14 days
C) 16 days
D) 24 days

Vijay Bharath Reddy
Let m be one man’s one day work and w be one woman’s one day work
Then 3m + 4w = 1/16 ………………..i
and 4m + 3w = 1/12 ……………….ii
From (i) & (ii) above
m = 1/48 and w = 0

Thus 2m + 5w = 2*1/48 + 5*0 = 1/24

So they will do the complete work in 24 days (option ‘D’)

QUERY 3

To do a certain work B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days . The time taken by A to complete the work separately.

A) 20 days
B) 24 days
C) 30 days
D) 35 days

Vijay Bharath Reddy
Let a, b, c be the number of days to be taken to finish the work by A, B & C respectively.
So according to the question
3/b = 1/a + 1/c …………………………………………….i
2/c = 1/a + 1/b …………………………………………….ii
1/a + 1/b + 1/c = 1/10 ……………………………………………iii
By solving the above we get c = 30, b = 40, and a = 24
Hence time taken by A alone = 24 days (option ‘B’)

QUERY 4

A and B together can do 11/19 of a work. In the same time B and C together can do 14/19 of the same work. The ratio of work done by A, B and C is ?

A) 5 : 6 : 7
B) 5 : 6 : 8
C) 6 : 5 : 8
D) 8 : 6 : 5

Vaibhav Vats
C’s work = 1 – Work of A + B
= 1 – 11/19 = 8/19

A’s work = 1 – Work of B + C
= 1 – 14/19 = 5/19

Now B’work = 1 – Work of A + C
= 1 – (5/19 + 8/19) = 1 – 13/19 = 6/19

So the Ratio of work done by A, B and C = 5/19 : 6/19 : 8/19
= 5 : 6 : 8 (option ‘B’)

TRICK
NITESH DUTT
Here in both the cases 19 is the divisor…….so it’s better to assume that value of the work of all three = 19

then;
A+B+C= 19
A+B= 11
B+C= 14
On solving we get A=5, B=6 and C=8

So the ratio = 5 : 6 : 8 (option ‘B’)

QUERY 5

8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in one day is double the work done by a woman in one day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined, in how many more days will the work completed?

A) 5 days
B) 6 days
C) 7 days
D) 8 days

MAHA GUPTA
8 men + 4 women
=> 8 men + 2 men = 10 men (as a man is double of a woman)

After 4 men have left and 4 women joined, the number of men is 4 and that of women is 8

So, 4 men + 8 women = 8 men

The work done by 10 men in 1 day = 1/6
The work done by them in 2 days = (1/6)*2 = 1/3
The work left to be done = 1 – 1/3 = 2/3

This work had to be done by 10 men in 4 days                                      —- 4 = 6 -2
Obviously, now it has to be finished by 4 men + 8 women
But that equals 8 men

Hence more number of days to be needed to finish the balance of the work = (4*10)/8 = 5 days (option ‘A’)

QUERY 6

Ram can do a work in 5 days less than the time taken by Shyam to do it. If both of them together take 100/9 days, then the time taken by Shyam alone to do the same work (in days) is?

A) 15
B) 25
C) 20
D) 30

NIKITA SHAH
Let time taken by Shyam = x days
So time taken by Ram = x – 5 days

Now Shyam’s 1 day work = 1/x
And Ram’s 1 day work = 1/(x – 5)
And their total work in 1 day = 9/100

Therefore 1/x + 1/(x – 5) = 9/100
Now instead of solving the equation algebraically try options in this equation as solving the equation that way will be time consuming; of course the answer you will be getting is 25 (option ‘B’).

 

QUERY 7

A can complete a work in 12 days, B in 15 days find time taken by them if A leaves two days before the scheduled completion of the work.

A) 9 days
B) 55/6 days
C) 29/3 days
D) 10 days

MAHA GUPTA
1 day work of A+B = 1/12 + 1/15 = 3/20
So total time taken by both to finish the work = 20/3 days (scheduled time)

But A leaves 2 days before the scheduled completion, so time for which ‘A’ works in actual = 20/3 – 2 = 14/3 days

Here we need to calculate how much work was finished in those 14/3 days.
Now, 1 day work of A+B = 1/12 + 1/15 = 3/20
Therefore work done by both of them working together in 14/3 days = (3/20)*(14/3) = 7/10

So the remaining work = 1 – 7/10 = 3/10
Obviously this work will have to be done by ‘B’ alone.

Now time taken by B to do 1/15 of the work = 1 day
So time taken by B to finish 3/10 of the work = 15*(3/10) = 9/2 days

Hence time taken by both to finish the work = 14/3 + 9/2 = 55/6 (option ‘B’)

 

QUERY 8

A contractor undertakes to do a piece of work in 40 days. He engages 100 men and after 35 days, an additional 100 men when complete the work. How many days behind schedule would he have been, had he not engaged the additional men?

A) 5 days
B) 8 days
C) 12 days
D) 15 days

MAHA GUPTA
Time remaining after 35 days = 40 – 35 = 5 days
Means 100 + 100 = 200 men finish the work in 5 days

Hence time that would have been taken if additional men were not employed i.e. 100 men = (200*5)/100 = 10 days

Therefore, days behind schedule would he have been, had he not engaged the additional men = 10 -5 = 5 days (option ‘A’)

QUERY 9

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

A) 20/3 days
B) 13 days
C) 40/3 days
D) 7 days

MAHA GUPTA
The work still left to be done = 1 – 7/10 = 3/10
But it was done by A & B both in 4 days
So time to be taken to do the entire work by both of them together = 4*10/3 = 40/3 days (option ‘C’)

QUERY 10

A can finish a job in 12 days, B in 20 days and C in 30 days. A, B & C start work together. After 3 days, A left. B+C worked for 2 days, then B left and A joined. A+C completed the remaining work. In how many days was the work finished?

A) 55/7 days
B) 20/7 days
C) 9 days
D) 20 days

MAHA GUPTA
Case-I when A, B and C all worked together for 3 days
Therefore their 3 days work = (1/12 + 1/20 + 1/30)*3 = (10/60)*3 = 1/2

Case-II when B and C worked together for 2 days
Therefore their 2 days work = (1/20 + 1/30)*2 = (5/60)*2 = 1/6

So total worked finished in these 5 days = 1/2 + 1/6 = 4/6 = 2/3
Now the remaining work that has to be done by A and C = 1 – 2/3 = 1/3

Now 1 day work of A and C if done together = 1/12 + 1/30 = 7/60

Time taken by them to complete 7/60 of work = 1 day
Therefore time to be taken by them to complete the remaining 1/3 of work = (60/7)*(1/3) = 20/7 days [By unitary method)

Hence the total time taken to finish the work = 5 + 20/7 = 55/7 days (option ‘A’)