# 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 |

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?

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 |

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 ?

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 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.

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