# Time and Work Questions

**FACTS AND FORMULAE FOR TIME AND WORK QUESTIONS**

**1. **If A can do a piece of work in n days, then A's 1 day's work =

**2. **If A’s 1 day's work =, then A can finish the work in n days.

**3. **A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

NOTE :

Hence,

Whole work is always considered as 1, in terms of fraction and 100% , in terms of percentage.

In general, number of day's or hours =

A) 200, 250, 300 | B) 300, 200, 250 |

C) 200, 300, 400 | D) None of these |

Explanation:

A's 5 days work = 50%

B's 5 days work = 33.33%

C's 2 days work = 16.66% [100- (50+33.33)]

Ratio of contribution of work of A, B and C =

= 3 : 2 : 1

A's total share = Rs. 1500

B's total share = Rs. 1000

C's total share = Rs. 500

A's one day's earning = Rs.300

B's one day's earning = Rs.200

C's one day's earning = Rs.250

A) 8 | B) 12 |

C) 16 | D) 24 |

Explanation:

1 man's 1 day work = ; 1 woman's 1 day work =

work done in 6 days=

Remaining work =

(8 men +8 women)'s 1 day work ==

Remaining work=

work is done in 1 day by 1 man

work will be done in 1 day by men

**Sol: **Ratio of efficiency = 2:1 (A:B)

Ratio of required time = 1:2 (A:B) x:2x

but 2x-x=30

x= 30 and 2x= 60

Now efficiency of A =3.33% and efficiency of B =1.66%

Combined efficiency of A and B together = 5%

time required by A and B working together to finish the work = = 20 days

Note: Efficiency

Efficiency time = Constant Work

Hence, Required time =

whole work is always cosidered as 1, in terms of fraction and 100%, in terms of percentage.

In, general no.of days or hours =

A) 11 days | B) 12 days |

C) 13 days | D) 14 days |

Explanation:

One day's work of A, B and C = (1/24 + 1/30 + 1/40) = 1/10

C leaves 4 days before completion of the work, which means only A and B work during the last 4 days.

Work done by A and B together in the last 4 days = 4 (1/24 + 1/30) = 3/10

Remaining Work = 7/10, which was done by A,B and C in the initial number of days.

Number of days required for this initial work = 7 days.

Thus, the total numbers of days required = 4 + 7 = 11 days.

A) 20days | B) 40 days |

C) 50 days | D) 60 days |

Explanation:

(A+B)'s 1 day's work=1/20

C's 1 day work=1/60

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

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

we get: 2 * (A's 1 day 's work)=1/15

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

B's 1 day's work=

So, B alone could do the work in 60 days.