# Important Formulas

# Problems on Time and Work

Q11. 10 men can finish the construction of a wall in 12 days. How many men are added to finish the work in half a day ?

(a) 120

(b) 220

(c) 230

(d) 240

**Answer:** (c) 230

Let the total number of men be x

No. of men 10 x

No. of day 12 1/2

Now 10 X 12 = x X (1/2) [proportion is inverse, More man less time taken]

=> x = (10 X 12)/(1/2) = 10 X 12 X 2 = 240

∴ Number of men to be added = (240 - 10) = 230

Q12. 20 men complete one third of a piece of work in 20 days. How many more men should be employed to finish the rest of the work in 25 more days ?

(a) 12

(b) 15

(c) 22

(d) 25

**Answer:** (a) 12

Work done = 1/3

Remaining work = (1 - 1/3) =2/3

Let the required number of men be x

1 | X 25 X (20+x) = | 2 | X 20 X 20 |

3 | 3 |

=> 20 + x = 800/25 = 32

=> x = 32 - 20 = 12

Q13. If 36 men can do a piece of work in 25 days, in how many days will 12 men do it ?

(a) 35

(b) 56

(c) 75

(d) 80

**Answer:** (c) 75

Let the required number of days be x

Now, 36 X 25 = 12 X x

⇒ x = (36 X 25)/12 = 75

Q14. The A Minar casts a shadow of 180m long at the same time when the B Minar casts a shadow of 120m long on the ground. If the height of the B Minar is 80m, what is the height of the A minar ?

(a) 105m

(b) 115m

(c) 120m

(d) 135m

**Answer:** (c) 120m

Let the required height of the A Minar be x m

A/Q x X 120 = 180 X 180

⇒ x = (180X180)/120 = 120m

Q15. 6 men can finish a piece of work in 30 days. If 3 men more join with them then the work will be completed in

(a) 18

(b) 20

(c) 22

(d) 24

**Answer:** (b) 20

Let the required time be x days

For 6 No. of Man = 30 No. of days

For 9 (6+3) No. of Man = x No. of days

A/Q 6 X 30 = 9 X x

⇒ x = (6X30)/9 = 20

Q16. 10 women can complete a work in 6 days and 10 children take 12 days to complete the work. How many days will 6 women and 4 children together take to complete the work ?

(a) 7½ days

(b) 8½ days

(c) 9½ days

(d) 10½ days

**Answer:** (a) 7½ days

10 women's 1 day's work = 1/6

1 women's 1 day's work = 1/60

6 women's 1 day's work = 6/60 = 1/10

10 children's 1 day's work = 1/12

1 children's 1 day's work = 1/120

4 children's 1 day's work = 4/120 = 1/30

∴ (6 women + 4 children) 1 day's work = 1/10 + 1/30 = 4/30

∴ They finish the work in 30/4 days = 7½ days

Q17. 5 men can complete a work in 10 days and the same work 6 women can complete in 15 days. How many days will 2 men and 3 women together take to complete the work ?

(a) 12(3/11) days

(b) 13(7/11) days

(c) 15(3/7) days

(d) 16(5/11) days

**Answer:** (b) 13(7/11) days

5 men's 1 day's work = | 1 |

10 |

1 men's 1 day's work = | 1 |

5 X 10 |

2 men's 1 day's work = | 2 | = | 1 |

50 | 25 |

6 women's 1 day's work = | 1 |

15 |

1 women's 1 day's work = | 1 |

6 X 15 |

3 women's 1 day's work = | 3 | = | 1 |

6 X 15 | 30 |

Now (2 Men + 3 Women)'s 1 day's work = | 1 | + | 1 | = | 6 + 5 | = | 11 |

25 | 30 | 150 | 150 |

∴ Required day's = 150/11 = 13(7/11) days

Q18. Ram can do a work in 15 days. Rahim is 50% more efficient than Ram. The number of days, Rahim will take to do the same piece of work is

(a) 7 days

(b) 8 days

(c) 10 days

(d) 13 days

**Answer:** (c) 10 days

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

Rahim's 1 day's work = 150% of 1/15

= | 150 | X | 1 |

100 | 15 |

= 1/10

Rahim can finish the work in 10 days.

Q19. Hari can do a work in 28 days. Jadu is 40% more efficient than Hari. The number of days, Jadu will take to do the same piece of work is

(a) 8 days

(b) 10 days

(c) 15 days

(d) 20 days

**Answer:** (d) 20 days

Hari's 1 day's work = 1/28

Jadu's 1 day's work = 140% of 1/28

= | 140 | X | 1 |

100 | 28 |

= 1/20

∴ Jadu can finish the work in 20 days.

Q20. A works twice fast as B. If both of them can together finish a piece of work in 15 days then B alone can do it in

(a) 28 days

(b) 33 days

(c) 37 days

(d) 45 days

**Answer:** (d) 45 days

Let, B's one day's work = x

∴ A's one day's work = 2x

(A + B)'s 1 day's work = x + 2x = 3x

A/Q 3x = 1/15

⇒ x = 1/(15 X 3) = 1/45

∴ B's one day's work = 1/45

∴ B alone can do it in 45 days