Time and Work problems
- 1. The rates of working of A and B are in the ratio 3 : 4. The number of days taken by them to finish the work are in the ratio?
Options- A. 3 : 4
- B. 9 : 16
- C. 4 : 3
- D. None of these Discuss
Correct Answer: 4 : 3
Explanation:
Radio of times taken = (1/3) : (1/4) = 4 : 3
- 2. A does half as much work as B in three-fourth of the time. If the together they take 18 days to complete a work. How much time shall B take to do it?
Options- A. 40 days
- B. 35 days
- C. 30 days
- D. None of these Discuss
Correct Answer: 30 days
Explanation:
Let B takes N days to do the work
? A takes 2 x (3/4) x N = 3N/2 days to do it
? (A + B)'s 1 day's work = 1/18
? 1/N + 2/3N = 1/18
? N = 30
- 3. A and B together can do a work in 24 days. B alone does its 1/3 part in 12 days. How long will A alone take to do the remaining work?
Options- A. 48 days
- B. 36 days
- C. 24 days
- D. 72 days Discuss
Correct Answer: 48 days
Explanation:
Work done by (A + B) in 1 day = 1/24
Work done by B alone in 1 day = 1/(3 x 12) = 1/36
? Work of A for 1 day = 1/24 - 1/36 = 1/72
After 12 days the remaining work = 1 - 1/3 = 2/3
? 1/72 work is done by A in 1 day
? 2/3 work is done by A in (1 x 72)/(1 x 2/3) = 48 days
- 4. 15 men complete a work in 16 days If 24 men are employed then the time require to complete that work will be
Options- A. 7 days
- B. 8 days
- C. 10 days
- D. 12 days Discuss
Correct Answer: 10 days
Explanation:
let the work done be 1 work.
Here M1=15, D1=16 W1=W2 =1
M2 =24 D2= ?
? According to the formula
M1 D1 W2 = M2 D2 W1
? 15 x 16 x 1 = 24 x D2 X 1
? D1 = 15 X 16/24 = 10
Therefore 10 days are required to complete the work
- 5. A can complete a piece of work in 18 days and B can complete the same work in half time taken by A. Then, working together, what part of the same work they can complete in a day?
Options- A. 1/6
- B. 1/9
- C. 2/5
- D. 2/7 Discuss
Correct Answer: 1/6
Explanation:
A's 1 day's work = 1/18
B's 1 day's work = 1/9
(A + B)'s 1 day's work = 1/9 + 1/18 = 3/18 = 1/6
- 6. A and B together can do a piece of work in 12 days, while B alone can finish it in 30 days. A alone can finish the work in?
Options- A. 15 days
- B. 18 days
- C. 20 days
- D. 25 days Discuss
Correct Answer: 20 days
Explanation:
(A + B)'s 1 days work = 1/12
B's 1 days work = 1/30
? A's 1 days work = 1/12 - 1/30 = (5 - 2)/60 = 1/20
? A alone can finish the work in 20 days.
- 7. Aarti can do a piece of work in 6 days. In how many days will she complete three time of work of same type?
Options- A. 18 days
- B. 21 days
- C. 3 days
- D. 6 days Discuss
Correct Answer: 18 days
Explanation:
We have the important relation, More work, More time (days)
? A piece of work can be done in 6 days.
? Three times of work of same type can be done in 6 x 3
= 18 days
- 8. A and B can do a piece of work in 6 and 12 days, respectively. They (both) will complete the work in how many days?
Options- A. 9 days
- B. 18 days
- C. 6 days
- D. 4 days Discuss
Correct Answer: 4 days
Explanation:
A's 1 day's work = 1/6
B's 1 day's work = 1/12
(A + B)'s 1 day's work = 1/6 + 1/12
= (2 + 1)/12 = 3/12 = 1/4
Hence, both will complete the work in 4 days.
- 9. If 3 men and 4 boys can do a piece of work in 8 day, then 6 men and 8 boys can do the same work in?
Options- A. 2 days
- B. 4 days
- C. 6 days
- D. 16 days Discuss
Correct Answer: 4 days
Explanation:
Let the men do the work in a days and the boys in b days.
? (3/a) + (4/b) = 1/8 ..... (i)
Now, 6/a + 8/b = 2[(3/a) + (4/b)] = 2 x 1/8 = 1/4
So, 6 men and 8 boys can do the same work in 4 days.
- 10. 'A' can do a piece of work in x days and B can do the same work 3x days. To finish the work together they take 12 days. What is the value of x?
Options- A. 8
- B. 10
- C. 12
- D. 16 Discuss
Correct Answer: 16
Explanation:
A's 1 day's work A = 1/x
B's 1 day's work B = 1/3x
(A + B)'s 1 day's work = (1/x) + (1/3x) = 4/3x
And given one day work of both A and B = 1/12
? 4/3x = 1/12
? 3x = 48
? x =16
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