1. | A can do a work in 15 days and B in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is : |

A's 1 day's work = | 1 | ; |

15 |

B's 1 day's work = | 1 | ; |

20 |

(A + B)'s 1 day's work = | 1 | + | 1 | = | 7 | . | ||

15 | 20 | 60 |

(A + B)'s 4 day's work = | 7 | x 4 | = | 7 | . | ||

60 | 15 |

Therefore, Remaining work = | 1 - | 7 | = | 8 | . | ||

15 | 15 |

2. | A can lay railway track between two given stations in 16 days and B can do the same job in 12 days. With help of C, they did the job in 4 days only. Then, C alone can do the job in: |

(A + B + C)'s 1 day's work = | 1 | , |

4 |

A's 1 day's work = | 1 | , |

16 |

B's 1 day's work = | 1 | . |

12 |

C's 1 day's work = | 1 | - | 1 | + | 1 | = | 1 | - | 7 | = | 5 | . | ||||

4 | 16 | 12 | 4 | 48 | 48 |

So, C alone can do the work in | 48 | = 9 | 3 | days. |

5 | 5 |

3. | A, B and C can do a piece of work in 20, 30 and 60 days respectively. In how many days can A do the work if he is assisted by B and C on every third day? |

A's 2 day's work = | 1 | x 2 | = | 1 | . | ||

20 | 10 |

(A + B + C)'s 1 day's work = | 1 | + | 1 | + | 1 | = | 6 | = | 1 | . | ||

20 | 30 | 60 | 60 | 10 |

Work done in 3 days = | 1 | + | 1 | = | 1 | . | ||

10 | 10 | 5 |

Now, | 1 | work is done in 3 days. |

5 |

Whole work will be done in (3 x 5) = 15 days.

4. | A is thrice as good as workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in: |

Ratio of times taken by A and B = 1 : 3.

The time difference is (3 - 1) 2 days while B take 3 days and A takes 1 day.

If difference of time is 2 days, B takes 3 days.

If difference of time is 60 days, B takes | 3 | x 60 | = 90 days. | ||

2 |

So, A takes 30 days to do the work.

A's 1 day's work = | 1 |

30 |

B's 1 day's work = | 1 |

90 |

(A + B)'s 1 day's work = | 1 | + | 1 | = | 4 | = | 2 | ||

30 | 90 | 90 | 45 |

A and B together can do the work in | 45 | = 22 | 1 | days. |

2 | 2 |

5. | A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs. 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C? |

C's 1 day's work = | 1 | - | 1 | + | 1 | = | 1 | - | 7 | = | 1 | . | ||

3 | 6 | 8 | 3 | 24 | 24 |

A's wages : B's wages : C's wages = | 1 | : | 1 | : | 1 | = 4 : 3 : 1. |

6 | 8 | 24 |

C's share (for 3 days) = Rs. | 3 x | 1 | x 3200 | = Rs. 400. | ||

24 |

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: |

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? |

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: |

(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 |

A's 1 day's work = | 3 | . |

50 |

B's 1 day's work | 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? |

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 |

B's 1 day's work = | 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 ? |

(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 2 hours. | ||

60 | 11 | 60 | 11 |

So, the work will be finished approximately 2 hours after 11 A.M., i.e., around 1 P.M.

11. | A can finish a work in 18 days and B can do the same work in 15 days. B worked for 10 days and left the job. In how many days, A alone can finish the remaining work? |

B's 10 day's work = | 1 | x 10 | = | 2 | . | ||

15 | 3 |

Remaining work = | 1 - | 2 | = | 1 | . | ||

3 | 3 |

Now, | 1 | work is done by A in 1 day. |

18 |

1 | work is done by A in | 18 x | 1 | = 6 days. | |||

3 | 3 |

12. | 4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it? |

Let 1 man's 1 day's work =

*x*and 1 woman's 1 day's work =*y*.Then, 4x + 6y = | 1 | and 3x + 7y = | 1 | . |

8 | 10 |

Solving the two equations, we get: x = | 11 | , y = | 1 |

400 | 400 |

1 woman's 1 day's work = | 1 | . |

400 |

10 women's 1 day's work = | 1 | x 10 | = | 1 | . | ||

400 | 40 |

Hence, 10 women will complete the work in 40 days.

13. | A and B can together finish a work 30 days. They worked together for 20 days and then B left. After another 20 days, A finished the remaining work. In how many days A alone can finish the work? |

(A + B)'s 20 day's work = | 1 | x 20 | = | 2 | . | ||

30 | 3 |

Remaining work = | 1 - | 2 | = | 1 | . | ||

3 | 3 |

Now, | 1 | work is done by A in 20 days. |

3 |

Therefore, the whole work will be done by A in (20 x 3) = 60 days.

14. | P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work? |

P can complete the work in (12 x 8) hrs. = 96 hrs.

Q can complete the work in (8 x 10) hrs. = 80 hrs.

P's1 hour's work = | 1 | and Q's 1 hour's work = | 1 | . |

96 | 80 |

(P + Q)'s 1 hour's work = | 1 | + | 1 | = | 11 | . | ||

96 | 80 | 480 |

So, both P and Q will finish the work in | 480 | hrs. | ||

11 |

Number of days of 8 hours each = | 480 | x | 1 | = | 60 | days = 5 | 5 | days. | ||

11 | 8 | 11 | 11 |

15. | 10 women can complete a work in 7 days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work? |

1 woman's 1 day's work = | 1 |

70 |

1 child's 1 day's work = | 1 |

140 |

(5 women + 10 children)'s day's work = | 5 | + | 10 | = | 1 | + | 1 | = | 1 | ||||

70 | 140 | 14 | 14 | 7 |

5 women and 10 children will complete the work in 7 days.

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