Practice Questions: Time and Work | Quantitative Techniques for CLAT PDF Download

Q1: A can do a piece of work in 10 days, and B can do the same work in 30 days. In how many days can the work be completed if A and B work together?
(a) 4 5 / 2
(b) 7 1 / 2
(c) 6 9 / 5
(d) 2 3 / 5
(e) None of these
Ans: (b)
A’s 1 day’s work = 1 / 10
B’s 1 day work = 1 / 30
Therefore,
(A + B)’s 1 day’s work = 1 / 10 + 1 / 30
(A + B)’s 1 day’s work = 2 / 15
Hence, A and B together can do the work in 15 / 2 days, i.e. 7 1 / 2 days.

Q2: A and B together can do a piece of work in 9 days. ‘A’ Alone can complete the work in 12 days. How long will B alone take to complete the job?
(a) 30 days
(b) 50 days
(c) 60 days
(d) 36 days
(e) 20 days
Ans: (d)
(A + B)’s 1 day’s work = 1 / 9
A’s Alone 1 day’s work = 1 / 12
Therefore,
B’s Alone 1 day’s work = 1 / 9 - 1/ 12
B’s Alone 1 day’s work = 1 / 36.
So, B alone can do the work in 36 days.

Q3: A can do work in 25 days. When he had worked for 15 days, B replaced him. If he completes the remaining work in 10 days, in how many days can B alone finish the work?
(a) 20 days
(b) 10 days
(c) 30 days
(d) 40 days
(e) None of these
Ans: (e)
A’s 1 day’s work = 1 / 25
A’s 15 day’s work = 15 / 25
A’s 15 day’s work = 3 / 5
Work remaining = (1 - 3 / 5) = 2 / 5 which is done by B in 10 days.
Therefore,
B can do the work alone in (5 / 2 x 10) = 25 days

Q4: A is thrice as good a workman as B and is therefore able to finish a piece of work in 30 days less than B. Find the time in which they can do it working together.
(a) 11 1 / 4
(b) 5 2 / 3
(c) 6 2 / 3
(d) 20 4 / 2
(e) None of these.
Ans: (a)
The ratio of work done by A and B in the same time = 3 : 1
Ratio of time taken by A and B = 1 : 3
Let B takes 𝑥 days to finish a work.
Then,
A takes (𝑥 - 30) days to finish it.
Therefore,
⇒ 𝑥 - 30 / 𝑥 = 1 / 3
⇒ 3𝑥 - 90 = 𝑥
⇒ 𝑥 = 45 days
Thus, A and B can finish the work in 15 days and 45 days, respectively.
Now, (A + B)’s 1 day’s work = 1 / 15 + 1 / 45 = 4 / 45.
So, both together can finish the work in 45 / 4 days = 11 1 / 4 days.

Q5: 1 woman or 2 men or 3 boys can do a piece of work in 55 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in how many days?
(a) 18 days
(b) 30 days
(c) 32 days
(d) 16 days
(e) None of these
Ans: (b)
1 woman = 2 man = 3 boys
⇒ 1 boy = 2 / 3 man.
⇒ 1 man + 1 woman + 1 boy = 1 man + 2 men + 2 / 3 men
 ⇒ (1 + 2 + 2 / 3) = 11 / 3 men.
If 2 men can do work in 55 days.
Then,
 ⇒ 11 / 3 men will do the same work in = 2 x 55 x 3 / 11 = 30 days.

Q6: If 5 men and 2 boys are working together, can do three times as much work per hour as a man and a boy together. The ratio of the work done by a man and that of a boy for a given time is
(a) 1 : 2
(b) 2 : 1
(c) 1 : 3
(d) 3 : 1
(e) None of these
Ans: (a)
⇒ 5 men + 2 boy = 3 (1 man + 1 boy)
⇒ 5 men + 2 boy = 3 men + 3 boy
⇒ 2 men = 1 boy
Therefore,
The required ratio of work done by a man and a boy = 1 : 2.

Q7: If 2 men and 3 boys can do a piece of work in 16 days and 3 men and 2 boys can do it in 14 days, how long will 5 men and 4 boys take to do it?
(a) 6 days
(b) 8 days
(c) 9 days
(d) 10 days
(e) None of these
Ans: (b)
⇒ 2 men + 3 boys = 16 days
⇒ 2 x 16 men + 3 x 16 boys = 1 day
⇒ 32 men + 48 boys = 1 day …………….. Equation (1)
And
⇒ 3 men + 2 boy = 14 days
⇒ 42 men + 28 boys = 1 day ………….. Equation (2)
On solving Equation (2), we get
⇒ 1 men = 2 boys
⇒ 2 men + 3 boys = 4 boys + 3 boys
⇒ 2 men + 3 boys = 7 boys
And
⇒ 5 men + 4 boys = 10 boys + 4 boys
⇒ 5 men + 4 boys = 14 boys
Now, 7 boys take = 16 days
Therefore,
⇒ 14 boys take = 16 x 7 / 14
 ⇒ 14 boys take = 8 day

Q8: A and B complete a piece of work in 5 days working together. If A had worked twice, the work would have been completed in 4 days. In how many days can A alone complete the work?
(a) 20 days
(b) 18 days
(c) 24 days
(d) 15 days
(e) None of these
Ans: (a)
Let A do the work in ‘a’ days.
A’s 1 day’s work = 1 / a
Let B do the work in ‘b’ days.
B’s 1 day’s work = 1 / b
Now,
⇒ 1 / a + 1 / b = 1 / 5 …………… Equation (1)
⇒ 2 / a + 1 / b = 1 / 4 ……………. Equation (2)
By solving Equation (1) and Equation (2), we get
⇒ a = 20 days.
Hence, A alone will complete the work in 20 days.

Q9: If I must hire 6 men and 8 boys for 6 days to do the same piece of work as 8 men and 15 boys could do in 4 days, compare the efficiency ratio of the men and the boys.
(a) 1 : 2
(b) 1 : 3
(c) 1 : 4
(d) 1 : 5
(e) None of these
Ans: (e)
⇒ (6 men + 8 boys) can do a piece of work in 6 days
⇒ (8 men + 15 boys) can do a piece of work in 4 days
⇒ (6 men + 8 boys) can do a piece of work in 6 days
⇒ (36 men + 48 boys) can do the work in 1 day
⇒ (8 men + 15 boys) can do a piece of work in 4 days
⇒ (32 men + 60 boys) can do the work in 1 day
⇒ 36 men + 48 boys = 32 men + 60 boys
⇒ 36 men - 32 men = 60 boys - 48 boys
⇒ 4 men = 12 boys
⇒ men = 3 boys
Therefore, the ratio of efficiency of men and boys = 3 : 1.

Q10: 3 men or 5 women can do work in 6 days. How long will 6 men and 5 women take to finish the work?
(a) 2.5 days
(b) 2 days
(c) 3 days
(d) 3.5 days
(e) None of these
Ans: (b)
3 men = 5 women
Or
⇒ 3 x 5 x 6 / (3 x 5 + 6 x 5)
⇒ 3 x 5 x 6 / 45 = 2
⇒ 1 man = 5 / 3 women
⇒ 6 men + 5 women = (6 x 5 / 3 + 5)
⇒ women = 15 women.
Now, if 5 women can do work in 6 days.
⇒ 15 women can do it in (5 x 6 / 15) days = 2 days
Hence, 6 men and 5 women will take 2 days to finish the work.

Q11: 4 men can do a piece of work in 10 days, 2 women can do it in 15 days and 5 children can do it in 12 days. In how many days can 8 men, 5 women and 15 children together complete the piece of work?
(a) 2 days
(b) 3 days
(c) 4 days
(d) 5 days
(e) None of these
Ans: (e)
⇒ 4 men’s 1 day’s work = 1 / 10.
⇒ 1 man’s 1 day’s work = 1 / 40.
⇒ 2 women’s 1 day’s work = 1 / 15.
⇒ 1 woman’s 1 day’s work = 1 / 30.
⇒ 5 children’s 1 day’s work = 1 / 12.
⇒ 1 child’s 1 day’s work = 1 / 60.
Now,
⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 8 / 40 + 5 / 30 + 15 / 60
⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 1 / 5 + 1 / 6 + 1 / 4
⇒ (8 men + 5 women + 15 children)’s 1 day’s work = 37 / 60.
So, they can finish the work in 60 / 37 days.

Q12: 3 men can do a piece of work in 12 days, 5 women in 8 days and 20 children in 3 days. In how many days can a man, a woman, and a child work together to complete the piece of work?
(a) 12 days
(b) 13 days
(c) 14 days
(d) 15 days
(e) None of these
Ans: (e)
⇒ 3 men can do a piece of work in 12 days
⇒ 1 man will do the same piece of work in 36 days.
⇒ 5 women can do a piece of work in 8 days.
⇒ 1 woman will do the same piece of work in 40 days
⇒ 20 children can do a piece of work in 3 days.
⇒ 1 child will do the same piece of work in 60 days.
Now,
⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 1 / 36 + 1 / 40 + 1 / 60
⇒ (1 man + 1 woman + 1 child)’s 1 day’s work = 5 / 72.
So, the work is complete in 72 / 5 days = 14 2 / 5 days

Q13: A certain number of men can complete a piece of work in 40 days. If there were 8 men more the work could be finished in 10 days less. How many men were there afterwards?
(a) 32 men
(b) 28 men
(c) 24 men
(d) 15 men
(e) None of these
Ans: (a)
Let the number of men be 𝑥.
𝑥 men can do a work in 40 days.
(𝑥 + 8) men can do the same work in (40 - 10) = 30 days.
⇒ 𝑥 x 40 = 30 (𝑥 + 8)
⇒ 40𝑥 = 30𝑥 + 240
⇒ 40𝑥 - 30𝑥 = 240
⇒ 10𝑥 = 240
⇒ 𝑥 = 24.
Therefore,
The number of men afterwards = 24 + 8 = 32 men

Q14: If A can d0 ¼ of the work in 4 days and B can do ⅛ of the work in 3 days, how much will A get if both work together and are paid Rs. 4,500 in all?
(a) Rs. 1,800
(b) Rs. 2,400
(c) Rs. 2,700
(d) Rs. 2,900
(e) None of these
Ans: (c)
Whole work is done by A in (4 x 4) days = 16 days
Whole work is done by Bin (8 x 3) days = 24 days.
A’s wages : B’s wages
⇒ A’s 1 day’s work : B’s 1 day's work
⇒ 1/16 : 1/24
⇒ 3 : 2
Therefore,
⇒ A’s sheet = (⅗ x 4,500)
⇒ A’s sheet = Rs. 2,700.

Q15: 6 men can complete a piece of work in 12 days. 8 women can do the same piece of work in 18 days whereas 18 children can complete it in 10 days. 4 men, 12 women and 20 children work together for 2 days. If only men were to complete the remaining work in 1 day, how many men would be required totally?
(a) 36 men
(b) 24 men
(c) 18 men
(d) Cannot be determined
(e) None of these
Ans: (a)
⇒ (6 x 12) men = (8 x 18) women = (18 x 10) children.
⇒ 2 men = 4 women = 5 children
Now, 4 men + 12 women + 20 children = 4 men + 6 men + 8 men = 18 men
⇒ 6 men’s 1 day’s work = 1/12
⇒ 18 men’s 1 day’s work = 1/12 x 18/6 = ¼
⇒ 18 men’s 2 day’s work = ¼ x 2
⇒ 18 men’s 2 day’s work = ½
Therefore,
The remaining work = 1 - ½
⇒ remaining work = ½
Remaining work can be complete by 18 men in 2 days
Therefore, to complete in 1 day, men required = 2 x 18 = 36 men.