# Important Formulas

# Problems on Time and Work

Q21. A alone can finish a work in 10 days which B alone can finish in 15 days. If they work together and finish it, then out of a total wages of Rs. 2000, A will get

(a) Rs. 1200

(b) Rs. 1300

(c) Rs. 1400

(d) Rs. 1500

**Answer:** (a) Rs. 1200

A's 1 day's work = 1/10

B's 1 day's work = 1/15

Ratio of wages of A and B = 1/10 : 1/15 = 3 : 2

∴ A's share = Rs. (2000 X (3/5)) = Rs. 1200

Q22. 12 women can complete a work in 8 days and 9 girl take 12 days to complete the work. How many days will 6 women and 9 girl take to complete the work ?

(a) 5(5/7) days

(b) 6(6/7) days

(c) 8(1/3) days

(d) 11(3/7) days

**Answer:** (b) 6(6/7) days

12 women's 1 day's work = 1/8

1 women's 1 day's work = 1/(12X8) = 1/96

6 women's 1 day's work = 6/96 = 1/16

9 girl's 1 day's work = 1/12

Now (6 women + 9 girl)'s 1 day's work = 1/16 + 1/12 = (3+4)/48 = 7/48

∴ Required time = 48/7 = 6(6/7) days

Q23. A man, a women and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a women take to complete the work ?

(a) 9 days

(b) 11 days

(c) 13 days

(d) 16 days

**Answer:** (a) 9 days

(1 man + 1 women + 1 boy)'s 1 day's work = 1/3

Let, a women take to complete the work in x days

Now | 1 | + | 1 | + | 1 | = | 1 |

6 | x | 18 | 3 |

⇒ | 1 | + | 1 | - | 1 | = - | 1 |

6 | 18 | 3 | x |

⇒ | 3 + 1 - 6 | = - | 1 |

18 | x |

⇒ | -2 | = - | 1 |

18 | x |

⇒ 1/x = 1/9

⇒ x = 9 days

Q24. 8 men working 8 hours a day can complete a piece of work in 14 days. In how many days can 6 men working for 9 hours a day, complete the same piece of work ?

(a) 13(11/29) days

(b) 16(16/27) days

(c) 17(13/17) days

(d) 19(3/11) days

**Answer:** (b) 16(16/27) days

8 men working 8 hours to complete in 14 days

∴ 1 men working 8 hours to complete in 14 X 8 days

1 men working 1 hour to complete in 14 X 8 X 8 days

∴ 6 men working 1 hour to complete in | 14 X 8 X 8 |

6 |

∴ 6 men working 9 hours to complete in | 14 X 8 X 8 | = | 448 | = 16 | 16 | days |

6 X 9 | 27 | 27 |

Q25. 9 children can complete a piece of work in 360 days; 18 men can complete the same piece of work in 72 days and 12 women can complete it in 162 days. In how many days can 4 men, 12 women and 10 children together complete the piece of work ?

(a) 57 days

(b) 66 days

(c) 71 days

(d) 81 days

**Answer:** (d) 81 days

18 men's 1 day's work = 1/72

1 men's 1 day's work = 1/(72X18) = 1/1296

12 women's 1 day's work = 1/162

∴ 1 women's 1 day's work = 1/(162X12) = 1/1944

9 children's 1 day's work = 1/360

1 children's 1 day's work = 1/(360X9) = 1/3240

Now (4 men + 12 women + 10 children)'s 1 day's work = | 4 | + | 12 | + | 10 | = ( | 1 | + | 1 | + | 1 | ) |

1296 | 1944 | 3240 | 324 | 162 | 324 |

= 4/324 = 1/81

Hence, required time = 81 days

Q26. If 6 men or 10 women can finish a piece of work in 20 days, 4 men and 5 women will do the same work in

(a) 14(1/7) days

(b) 15(1/7) days

(c) 17(1/7) days

(d) 19(1/7) days

**Answer:** (c) 17(1/7) days

6 men's 1 day's work = 1/20

∴ 1 men's 1 day's work = 1/(20X6)

∴ 4 men's 1 day's work = 4/(20X6) = 1/30

10 women's 1 day's work = 1/20

1 women's 1 day's work = 1/(20X10)

5 women's 1 day's work = 5/(20X10) = 1/40

∴ (4 men + 5 women)'s 1 day's work = 1/30 + 1/40 = (4+3)/120 = 7/120

∴ Required time = 120/7 = 17(1/7) days

Q27. A can do ¼ th part of the work in 10 days. B can do 40% of the work in 40 days and c can do 1/3rd of the work in 13 days. Who will complete the work first ?

(a) A

(b) B

(c) C

(d) All will complete the work on same time

**Answer:** (c) C

¼ th of the work is done by A in 10 days

∴ Whole work can be done by A in 40 days

40/100 of the work is done by B in 40 days

∴ Whole work can be done by B in 100 days

1/3 rd of the work is done by C in 13 days

∴ whole work will be done by C in = 39 days

Hence C will complete the work first

Q28. A can build a wall in 30 days, while B alone can build it in 40 days. If they build it together and get a payment of Rs. 14000, what is B's share ?

(a) Rs. 5000

(b) Rs. 6000

(c) Rs. 6500

(d) Rs. 7000

**Answer:** (b) Rs. 6000

A's 1 day's work = 1/30

B's 1 day's work = 1/40

Ratio of shares of A and B = 1/30 : 1/40 = 4 : 3

∴ B's sahre = Rs. (14000 X (3/7)) = Rs. 6000

Q29. A can do a piece of work in 50 days which B alone can finish in 40 days. Both together work for 10 days and then A leaves off. How many days will B take to finish the remaining work ?

(a) 15 days

(b) 18 days

(c) 19 days

(d) 22 days

**Answer:** (d) 22 days

(A+B)'s 1 day's work = (1/50 + 1/40) = 9/200

∴ (A+B)'s 10 day's work = | 9 X 10 | = | 9 |

200 | 20 |

Remaining work = 1 - | 9 | = | 11 |

20 | 20 |

1/40 work is done by B in 1 day

∴ 1 work is done by B in = 40 day

∴ 11/20 work is done by B = 40 X (11/20) days = 22 days

Q30. A can do a piece of work in 18 days which B can do it in 10 days. B work at it for 9 days. A can finish the remaining work in

(a) 1(4/5) days

(b) 3¾ days

(c) 3½ days

(d) 5½ days

**Answer:** (a) 1(4/5) days

A's 1 day's work = 1/18

B's 1 day's work = 1/10

B's 9 day's work = 9/10

Remaining work = 1 - | 9 | = | 1 |

10 | 10 |

1/18 work is done by A in 1 day

∴ 1 work is done by A in 18 days

∴ 1/10 work is done by A in = 18 X (1/10) = 1(4/5) days