# Important Formulas

# Problems on Time and Work

Q1. A can do a work in 4 days and B can do the same work
in 3 days. How long it will take if both A and B do the work
together ?

(a) 1 days

(b) 1 days 5/7 hours

(c) 2 days 3 hours

(d) 3 days

**Answer:** (b) 1 days 5/7 hours

A's 1 day's work = 1/4 and B's 1 day's work = 1/3

So (A+B)'s 1 day's work = (1/4 + 1/3) = 7/12

So A and B will finish the work in 12/7 = 1 days 5/7 hours

Q2. A and B complete a work in 6 days. If can A can
complete the work in 14 days, in how many days B alone can
do the same work.

(a) 1 days

(b) 1 days 5/7 hours

(c) 2 days 3 hours

(d) 3 days

**Answer:** (b) 1 days 5/7 hours

(A+B)'s 1 day work = 1/6 and A's 1 day's work = 1/14

So B's 1 day work = (1/6 - 1/14) = 4/42

So B can finish the work in 42/4 = 10.5 days

Q3. A and B can complete a work in 30 days, while B and C
do the same work in 24 days and C and A do the same work on
20 days. They all work together for 10 days and after that B
and C leave the work. How many days more will A take to
finish the work ?

(a) 12 days

(b) 13 days

(c) 16 days

(d) 18 days

**Answer:** (d) 18 days

2(A+B+C)'s 1 day work = (1/30 + 1/24 + 1/20) = 15/20 = 1/8

So (A+B+C)'s 1 day work = 1/16

So work done by A+B+C in 10 days = 10/16 = 5/8

Remaining Work = (1- 5/8) = 3/8

A's 1 day work = ( 1/16 - ((B+C)'s 1 day work capacity)) = ( 1/16 - 1/24) = 1/48

So 3/8 work will be done by A in (48 X 3/8) = 18 days

Q4. A can do a piece of work in 20 days. He works it for
4 days and then B finish the work in 12 days. How long will
it takes if both A and B works together ?

(a) 6 days

(b) 8.5 days

(c) 10.3 days

(d) 12 days

**Answer:** (b) 8.5 days

Work done by A in 1 day = 1/20

So work done by A in 8 days = (1/20 X 4) = 1/5

Remaining work = (1 - 1/5) = 4/5

Now 4/5 work done by B in 12 days

So whole work done will be done by B in (12 X 5/4)= 15 days

A's 1 day's work = 1/20 and B's 1 day's work=1/15

(A+B)'s 1 day's work = (1/20 + 1/15) = 7/60

So A and B will complete the work in 60/7 =8.5 days

Q5. A and B together can complete a piece of work in 72
days, B and C together in 120 days and A and C together in
90 days. A, B and C together can complete the work in ?

(a) 35 days

(b) 40 days

(c) 48 days

(d) 60 days

**Answer:** (d) 60 days

(A + B)'s 1 day's work = 1/72

(B + C)'s 1 day's work = 1/120

(A + C)'s 1 day's work = 1/90

2(A + B + C)'s 1 day's work = 1/70 + 1/120 + 1/90

2(A + B + C)'s 1 day's work = 1/30

(A + B + C)'s 1 day's work = 1/60

So A, B and C can together complete the work in 60 days

Q6. A can complete a work in 2 days and B can complete
the work in 3 days. With the help of C they together
completed in 1 day. C alone can complete the work in ?

(a) 2 days

(b) 4 days

(c) 6 days

(d) 7 days

**Answer:** (c) 6 days

If C alone can finish the work in x days, then

1/2 + 1/3 + 1/x = 1

1/x = 1 - 1/2 - 1/3

1/x = 1/6

So C alone can finish the work in 6 days.

Q7. A can complete a work in 15 days and B can complete
the work in 20 days. If B works for 8 days and left the job,
then in how many days the A can complete the remaining job ?

(a) 6 days

(b) 7 days

(c) 8 days

(d) 9 days

**Answer:** (d) 9 days

A's 1 day's work = 1/15 and B's 1 day's work = 1/20

So work done by B in 8 days = (1/20 X 8) = 2/5

Remaining work to be done = (1 - 2/5) = 3/5

1/15 work done by A in 1 day

So 3/5 work done by A in = (3/5 X 15) = 9 days

Q8. Ram and Rohit together can finish a job in 10 days. Ram can do the same job on his own in 12 days. How long will Rohit take to do the job by himself

(a) 40 days

(b) 60 days

(c) 80 days

(d) 100 days

**Answer:** (b) 60 days

(Ram + Rohit)'s 1 day's work = 1/10

Ram's 1 day's work = 1/12

∴ Rohit's 1 day's work = (1/10) - (1/12) = (6-5)/60 = 1/60

∴ Rohit can finish the work in 60 days

Q9. A does 20% less work than B. If A can complete a piece of work in 7(1/2) hours, then B can do it in

(a) 4 hrs

(b) 5 hrs

(c) 6 hrs

(d) 8 hrs

**Answer:** (c) 6 hrs

A can complete the work in = 7(1/2) hrs = 15/2 hrs

∴ B can complete the work in 7(1/2) h - 7(1/2) X 20% h

= | 15 | h - | 15 | X | 20 | h |

2 | 2 | 100 |

= | 15 | (1 - | 20 | ) h |

2 | 100 |

= | 15 | X | 80 | = 6hrs |

2 | 100 |

Q10. 4 men or 6 women can do a work in 12 days. How long will 6 men and 6 women take to finish the work

(a) 4 days

(b) 4(4/5) days

(c) 5(1/2) days

(d) 4(1/2) days

**Answer:** (b) 4(4/5) days

4 men = 6 women

1 men = 6/4 women

6 men = (6/4) X 6 = 9 women

6 women can do the work in 12 days

∴ 1 women can do the work in = 12 X 6 days = 72 days

∴ 6 men + 6 women = 9 women + 6 women = 15 women

Now 15 women can do the work in (72/15) days = 4(12/15) days = 4(4/5) days