Aptitude - Time and Work
Exercise : Time and Work - General Questions
- Time and Work - Formulas
- Time and Work - General Questions
- Time and Work - Data Sufficiency 1
- Time and Work - Data Sufficiency 2
- Time and Work - Data Sufficiency 3
6.
If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:
Answer: Option
Explanation:
Let 1 man's 1 day's work = x and 1 boy's 1 day's work = y.
Then, 6x + 8y = | 1 | and 26x + 48y = | 1 | . |
10 | 2 |
Solving these two equations, we get : x = | 1 | and y = | 1 | . |
100 | 200 |
(15 men + 20 boy)'s 1 day's work = | ![]() |
15 | + | 20 | ![]() |
= | 1 | . |
100 | 200 | 4 |
15 men and 20 boys can do the work in 4 days.
7.
A can do a piece of work in 4 hours; B and C together can do it in 3 hours, while A and C together can do it in 2 hours. How long will B alone take to do it?
Answer: Option
Explanation:
A's 1 hour's work = | 1 | ; |
4 |
(B + C)'s 1 hour's work = | 1 | ; |
3 |
(A + C)'s 1 hour's work = | 1 | . |
2 |
(A + B + C)'s 1 hour's work = | ![]() |
1 | + | 1 | ![]() |
= | 7 | . |
4 | 3 | 12 |
B's 1 hour's work = | ![]() |
7 | - | 1 | ![]() |
= | 1 | . |
12 | 2 | 12 |
B alone will take 12 hours to do the work.
8.
A can do a certain work in the same time in which B and C together can do it. If A and B together could do it in 10 days and C alone in 50 days, then B alone could do it in:
Answer: Option
Explanation:
(A + B)'s 1 day's work = | 1 |
10 |
C's 1 day's work = | 1 |
50 |
(A + B + C)'s 1 day's work = | ![]() |
1 | + | 1 | ![]() |
= | 6 | = | 3 | . .... (i) |
10 | 50 | 50 | 25 |
A's 1 day's work = (B + C)'s 1 day's work .... (ii)
From (i) and (ii), we get: 2 x (A's 1 day's work) = | 3 |
25 |
![]() |
3 | . |
50 |
![]() |
![]() |
1 | - | 3 | ![]() |
= | 2 | = | 1 | . |
10 | 50 | 50 | 25 |
So, B alone could do the work in 25 days.
9.
A does 80% of a work in 20 days. He then calls in B and they together finish the remaining work in 3 days. How long B alone would take to do the whole work?
Answer: Option
Explanation:
Whole work is done by A in | ![]() |
20 x | 5 | ![]() |
= 25 days. |
4 |
Now, | ![]() |
1 - | 4 | ![]() |
i.e., | 1 | work is done by A and B in 3 days. |
5 | 5 |
Whole work will be done by A and B in (3 x 5) = 15 days.
A's 1 day's work = | 1 | , (A + B)'s 1 day's work = | 1 | . |
25 | 15 |
![]() |
![]() |
1 | - | 1 | ![]() |
= | 4 | = | 2 | . |
15 | 25 | 150 | 75 |
So, B alone would do the work in | 75 | = 37 | 1 | days. |
2 | 2 |
10.
A machine P can print one lakh books in 8 hours, machine Q can print the same number of books in 10 hours while machine R can print them in 12 hours. All the machines are started at 9 A.M. while machine P is closed at 11 A.M. and the remaining two machines complete work. Approximately at what time will the work (to print one lakh books) be finished ?
Answer: Option
Explanation:
(P + Q + R)'s 1 hour's work = | ![]() |
1 | + | 1 | + | 1 | ![]() |
= | 37 | . |
8 | 10 | 12 | 120 |
Work done by P, Q and R in 2 hours = | ![]() |
37 | x 2 | ![]() |
= | 37 | . |
120 | 60 |
Remaining work = | ![]() |
1 - | 37 | ![]() |
= | 23 | . |
60 | 60 |
(Q + R)'s 1 hour's work = | ![]() |
1 | + | 1 | ![]() |
= | 11 | . |
10 | 12 | 60 |
Now, | 11 | work is done by Q and R in 1 hour. |
60 |
So, | 23 | work will be done by Q and R in | ![]() |
60 | x | 23 | ![]() |
= | 23 | hours ![]() |
60 | 11 | 60 | 11 |
So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.
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