Question: .If 20 men take 30 days to complete a job.In how many
days can 25 men complete the job?
a)28 days b)24 days c)36 days d)20 days
2.Fifteen men take 10 days to complete a job working 12
hours a day.How many hours a day
should 10 men work to complete the job in 20 days?
a)20 days b)8 days c)9 days d)10 days
3.A piece of work can be done by 16 men in 8 days working
12 hours a day.How many men are
needed to complete another work, which is three times the
first one,in 24 days working 8
hours a day?
a)24 men b)29 men c)20 men d)30 men
4.A can do a piece of work in 9 days.,B can do the same in
12 days.In how many days can the
work be completed if A and B work together?
a)5 1/9 days b)5 1/4 days c)5 1/3 days d)5 1/7 days
5.A and B together can do a piece of work in 12 days and A
alone can complete the work in 18
days. How long will B alone take to complete the job?
a)30 days b)36 days c)6 days d)56 days
6.Anil and Amit can complete a job in 12 days working
together. Amit alone can complete it in
16 days.Both of them worked together for 4 days and then
Amit left. How long will Anil take
to complete the remaining work?
a)30 days b)47 days c)32 days d)24 days
7.A and B can do a piece of work in 12 days,B and C can do
it in 15 days and C and A can do
the same work in 20 days. How long would each take to
complete the job?
a)1/30,1/20,1/60 b)1/20,1/30,1/30 c)1/20,1/20,1/20
d)1/60,1/0,1/30
8.A and B can do a work in 12 days,B and C in 15 days and C
and A in 20 days.They all work
together for 6 days and then A left.In how many more days
can B and C finish the remaining
work?
a)5 days b)6 days c)8 days d)9 days
9.A can do a work in 12 days.When he had worked for 3 days
B joined him.If they complete the
work in 3 more days.In how many days can B alone can
finish the work?
a)5 days b)6 days c)8 days d)9 days
10.A and B together can do a piece of work in 14 2/5 days;B
and C together can do the same
work in 12 days.After A worked for 8 days,B for 12 days C
takes up and finished it alone
in 6 days.In how many days will each of them do the
work,working alone?
a)28 days b)24 days c)36 days d)20 days
11.To do a certain work C alone takes twice as long as A and
B together.A would take 3 times
as long as B and C together.All three together complete
the work in 5 days.How long would
each take separately?
a)15 days b)29 days c)20 days d)10 days
12.4 men or 5 women can construct a wall in 82 days.How
long will it take 5 men and 4 women to
do the same?
a)30 days b)47 days c)32 days d)40days
13.If 9 men and 12 boys can do a piece of work in 4 days
and 4 men and 16 boys can do the same
piece of work in 6 days.how long will 6 men and 24 boys
take to complete the same work?
a)5 days b)6 days c)8 days d)4 days
14.A certain number of men can do a work in 20 days.If
there were 4 more men,the work can be
done in 5 days less.How many men were there initially?
a)12 days b)18 days c)16 days d)4 days
15.X is 3 times as fast as Y and is able to complete the work
in 40 days less than Y.Find the
time in which they can complete the work together?
a)12 days b)17 days c)19 days d)15 days
16.Sita can finish some work in 12 days working 4 hours a
day.Gita can finish the same in 15
days working 3 hours a day.In how many days can they
finish it working together at 4 1/2
hours a day?
a)5 5/31 days b)5 5/32 days c)5 5/33 days
d)5 5/34 days
17.A alone can do a work in 12 days and B alone in 18
days.If C takes twice as long as A and B
together,how long will B and C together take to complete
the same work?
a)5 days b)6 days c)8 days d)4 days
18.A and B each working alone can do a work in 10 and 15
days respectively.They started the work
together but B left after sometime and A finished the
remaining work in 5 days.After how many
days from the start did B leave?
a)4 days b)3 days c)2 days d)8 days
19.A contractor decided to complete the work in 40 days and
employed 60 men at the beginning and
40 men additionally after 10 days and got the work
completed as per schedule.If he had not
employed the additional men,how many extra days would
he have needed to complete the work?
a)30 days b)20 days c)40 days d)45 days
20.A group of 35 men is employed to complete some work in
48 days.After 33 days,5 more men are
employed and the work is finished 1 day ealier.If 5 more
men were not employed,how many more
days would it have taken beyond the expected period?
a)7 day behind schedule
b)3 day behind schedule
c)2 day behind schedule
d)1 day behind schedule
21.A and B working separately can do a piece of work in 6
and 9 days respectively;they work on
althernate days starting with A on the first day.In how
many days will the work be done?
a)4 days b)3 days c)2 days d)7 days
22.A and B working separately can do a piece of work in 6
and 12 days respectively.They work on
alternate days starting with A on the first day.In how many
days will the work be completed?
a)4 days b)3 days c)2 days d)8 days
23.A and B working separately,can do a piece of work in 12
and 15 days .They work on alternate
days starting with A on the first day.In how many days will
the work be completed?
a13 1/4 days b)13 2/4 days c)13 3/4 days
d)135/4 days
24.A and B working separately can do a piece of work in 20
and 24 days.They work on alternate
days starting with B on the first day.In how many days will
the work be completed?
a)21 5/6 days b)21 1/6 days c)21 4/5 days
d)none of these
25.A ,B and C can do a piece of work in 4,5 and 7 days
respectively.They got Rs.415 for the job.
what is A's share?
a)120 b)175 c)160 d)140
26.A,B and C contract a work for Rs.4500.A and B together
complete 3/5th of the work and then C
takes over and finished the work.What is the amount got
by C?
a)1200 b)1800 c)1600 d)1400
27.Wages for 40 women for 30 days are Rs,21,600.How
many men must work for 25 days to earn Rs.
14,400 if the daily wages for a man are double that of a
women?
a)12 b)14 c)16 d)19
28.A,B and C can together earn Rs.1,620 in 9 days.A and C
can earn Rs.600 in 5 days where as B and
C in 7 days can earn Rs 910.Find the daily earnings of C?
a)Rs 60 b)Rs 70 c)Rs 80 d)Rs 90
29.A can do a piece of work in 20 days and B in 30 days.A
starts the work and worked for 6 days.
Then B completed the remaining part of the work.In how
many days was the work completed?
a)24b)27 c)32 d)34
30.A can do a piece of work in 24 days and B in 48 days.B
joins A after A had worked alone for
6 days.In how many more days would the work get
completed?
a)10b)11 c)12 d)13
31.P can complete a piece of work in 20 days and Q in 30
days.P worked alone for 4 days and then
Q completed the remaining work along with R in 18
days.In how many days can R working alone
complete the work?
a)60b)65 c)80 d)90
32.25 men take 25 days to construct a wall 10 m high.How
many men would be required to construct a
similar wall,which is 8 m high,if it is planned that the work
would be completed in 10 days?
a)32b)40 c)44 d)48
33.20 cows and 40 goats can be kept for 10 days for
Rs.460.What would be the cost of keeping 50
cows and 30 goats for 12 days if the cost of keeping 5
goats is the same as cost of keeping
1 cow?
a)Rs 888 b)Rs 965 c)Rs 1007 d)Rs 1104
34.A,B and C started the work and after completing 1/5th of
the work C left.A and B then worked
for 20 days.C then took over from A and B and completed
the remaining portion of the work in
12 days.If C takes 40 days to complete the work , in how
many days wourd A alone or B alone
complete the work if the efficiencies with which they work
is the same?
a)40b)60 c)80 d)100
35.A boy is trying to cover a distance of 100 meters.He takes
a jump forward and covers 2m,but
every time he jumps forward he also moves 1m
backward.In all,how many jumps would be required
to cover the distance?
a)99b)100 c)98 d)none of these
36.A piece of work can be completed by 10 men in certain
number of days.If there were 2 men less
it would have taken 3 more days to complete the work.In
how many days can 24 men complete the
same work?
a)2 b)3 c)4 d)5
37.A is 80 % more efficient than B who is 60% more efficient
than C.A takes 40 days less than B to
complete a work. A starts the work and works for 25 days
and then B takes over.B then work for
the next 30 days and then stops.In how much more time
can C complete the remaining work?
a)20 days b)24 days c)32 days d)40 days
38.3 men and 5 women can complete a work in 12 days
,which 5 men and 12 women can complete in 6
days.In how many days can 4 men and 4 women complete
the same work?
a)7 b)10 c)11 d)12
39.P and Q agreed to complete a job in 15 days for Rs
6200.P can complete the same job in 50 days
and Q in 30 days.They had to take R to complete the work
in time.Find R's share in the money
earned by them.
a)Rs 880 b)Rs 1240 c)Rs 1460 d)Rs 2020
40.A and B complete a piece of work in 10 days.B and C in
12 days and C and A in 15 days.All the
three of them started working and then B left after 4
days.C left 3 days after that and then
immediately B joined A again to complete the remaining
work.In how many days was the work
completed?
a)10b)12 c)14 d)22
1. Problem: If $20$ men take $30$ days to complete a job, in how many days can $25$ men complete the job?
2. Formula: Work done is inversely proportional to the number of men and days, so $\text{Men}_1 \times \text{Days}_1 = \text{Men}_2 \times \text{Days}_2$.
3. Calculation:
$$20 \times 30 = 25 \times x$$
$$600 = 25x$$
$$x = \frac{600}{25} = 24$$
4. Answer: $25$ men can complete the job in $24$ days.
---
1. Problem: Fifteen men take $10$ days working $12$ hours a day. How many hours a day should $10$ men work to complete the job in $20$ days?
2. Formula: Total work = men $\times$ days $\times$ hours per day.
3. Calculation:
$$15 \times 10 \times 12 = 10 \times 20 \times h$$
$$1800 = 200h$$
$$h = \frac{1800}{200} = 9$$
4. Answer: $10$ men should work $9$ hours a day.
---
1. Problem: $16$ men can do a work in $8$ days working $12$ hours a day. How many men are needed to complete another work, which is three times the first one, in $24$ days working $8$ hours a day?
2. Formula: Work = men $\times$ days $\times$ hours.
3. Calculation:
First work units:
$$16 \times 8 \times 12 = 1536$$
Second work units:
$$3 \times 1536 = 4608$$
Let $x$ be the number of men needed:
$$x \times 24 \times 8 = 4608$$
$$192x = 4608$$
$$x = \frac{4608}{192} = 24$$
4. Answer: $24$ men are needed.
---
1. Problem: A can do a piece of work in $9$ days, B in $12$ days. How many days if they work together?
2. Formula: Work rate combined = $\frac{1}{9} + \frac{1}{12} = \frac{4}{36} + \frac{3}{36} = \frac{7}{36}$ per day.
3. Calculation:
$$\text{Days} = \frac{1}{\frac{7}{36}} = \frac{36}{7} = 5 \frac{1}{7}$$
4. Answer: $5 \frac{1}{7}$ days.
---
1. Problem: A and B together can do a work in $12$ days; A alone in $18$ days. How long will B alone take?
2. Formula:
$$\frac{1}{A+B} = \frac{1}{12}, \quad \frac{1}{A} = \frac{1}{18}$$
3. Calculation:
$$\frac{1}{B} = \frac{1}{12} - \frac{1}{18} = \frac{3-2}{36} = \frac{1}{36}$$
4. Answer: B alone takes $36$ days.
---
1. Problem: Anil and Amit can complete a job in $12$ days together; Amit alone in $16$ days. They worked together for $4$ days, then Amit left. How long will Anil take to complete the remaining work?
2. Formula:
$$\frac{1}{Anil + Amit} = \frac{1}{12}, \quad \frac{1}{Amit} = \frac{1}{16}$$
3. Calculation:
Anil's rate:
$$\frac{1}{Anil} = \frac{1}{12} - \frac{1}{16} = \frac{4-3}{48} = \frac{1}{48}$$
Work done in $4$ days together:
$$4 \times \frac{1}{12} = \frac{1}{3}$$
Remaining work:
$$1 - \frac{1}{3} = \frac{2}{3}$$
Time for Anil alone:
$$\frac{2/3}{1/48} = 32$$
4. Answer: Anil will take $32$ days.
---
1. Problem: A and B can do a work in $12$ days, B and C in $15$ days, C and A in $20$ days. Find time taken by each alone.
2. Formula:
Let rates be $a, b, c$ per day.
$$a + b = \frac{1}{12}, \quad b + c = \frac{1}{15}, \quad c + a = \frac{1}{20}$$
3. Calculation:
Add all:
$$2(a + b + c) = \frac{1}{12} + \frac{1}{15} + \frac{1}{20} = \frac{5}{60} + \frac{4}{60} + \frac{3}{60} = \frac{12}{60} = \frac{1}{5}$$
$$a + b + c = \frac{1}{10}$$
Find each:
$$a = (a+b+c) - (b+c) = \frac{1}{10} - \frac{1}{15} = \frac{3-2}{30} = \frac{1}{30}$$
$$b = (a+b+c) - (c+a) = \frac{1}{10} - \frac{1}{20} = \frac{2-1}{20} = \frac{1}{20}$$
$$c = (a+b+c) - (a+b) = \frac{1}{10} - \frac{1}{12} = \frac{6-5}{60} = \frac{1}{60}$$
4. Answer: A takes $30$ days, B takes $20$ days, C takes $60$ days.
---
1. Problem: A and B can do a work in $12$ days, B and C in $15$ days, C and A in $20$ days. They work together for $6$ days, then A leaves. How many more days will B and C take to finish?
2. Formula:
From previous problem:
$$a = \frac{1}{30}, b = \frac{1}{20}, c = \frac{1}{60}$$
3. Calculation:
Work done in $6$ days by all:
$$(a + b + c) \times 6 = \frac{1}{10} \times 6 = \frac{3}{5}$$
Remaining work:
$$1 - \frac{3}{5} = \frac{2}{5}$$
Rate of B and C:
$$b + c = \frac{1}{20} + \frac{1}{60} = \frac{3+1}{60} = \frac{4}{60} = \frac{1}{15}$$
Time to finish remaining:
$$\frac{2/5}{1/15} = 6$$
4. Answer: B and C will take $6$ more days.
---
1. Problem: A can do a work in $12$ days. He worked for $3$ days, then B joined. They finished the work in $3$ more days. How long can B alone do the work?
2. Formula:
A's rate: $\frac{1}{12}$ per day.
3. Calculation:
Work done by A in $3$ days:
$$3 \times \frac{1}{12} = \frac{1}{4}$$
Remaining work:
$$1 - \frac{1}{4} = \frac{3}{4}$$
Let B's rate be $b$.
Together for $3$ days:
$$3 \times \left(\frac{1}{12} + b\right) = \frac{3}{4}$$
$$\frac{3}{12} + 3b = \frac{3}{4}$$
$$\frac{1}{4} + 3b = \frac{3}{4}$$
$$3b = \frac{1}{2}$$
$$b = \frac{1}{6}$$
4. Answer: B alone can finish in $6$ days.
---
1. Problem: A and B together can do a work in $14 \frac{2}{5}$ days; B and C in $12$ days. After A worked $8$ days, B $12$ days, C finished alone in $6$ days. Find time taken by each alone.
2. Formula:
Let rates be $a, b, c$.
$$\frac{1}{a+b} = \frac{1}{14 \frac{2}{5}} = \frac{1}{\frac{72}{5}} = \frac{5}{72}$$
$$\frac{1}{b+c} = \frac{1}{12}$$
3. Calculation:
Work done by A in $8$ days:
$$8a$$
By B in $12$ days:
$$12b$$
By C in $6$ days:
$$6c$$
Total work:
$$8a + 12b + 6c = 1$$
From equations:
$$a + b = \frac{5}{72}$$
$$b + c = \frac{1}{12}$$
Express $a = \frac{5}{72} - b$, $c = \frac{1}{12} - b$.
Substitute:
$$8\left(\frac{5}{72} - b\right) + 12b + 6\left(\frac{1}{12} - b\right) = 1$$
Simplify:
$$\frac{40}{72} - 8b + 12b + \frac{6}{12} - 6b = 1$$
$$\frac{40}{72} + \frac{6}{12} - 2b = 1$$
$$\frac{40}{72} + \frac{36}{72} - 2b = 1$$
$$\frac{76}{72} - 2b = 1$$
$$-2b = 1 - \frac{76}{72} = \frac{72}{72} - \frac{76}{72} = -\frac{4}{72} = -\frac{1}{18}$$
$$b = \frac{1}{36}$$
Then:
$$a = \frac{5}{72} - \frac{1}{36} = \frac{5}{72} - \frac{2}{72} = \frac{3}{72} = \frac{1}{24}$$
$$c = \frac{1}{12} - \frac{1}{36} = \frac{3}{36} - \frac{1}{36} = \frac{2}{36} = \frac{1}{18}$$
4. Answer: A takes $24$ days, B takes $36$ days, C takes $18$ days.
---
1. Problem: To do a work C alone takes twice as long as A and B together. A takes 3 times as long as B and C together. All three together complete the work in 5 days. Find time taken by each alone.
2. Formula:
Let rates be $a, b, c$.
Given:
$$c = \frac{1}{2(a+b)}$$
$$a = 3(b+c)$$
$$a + b + c = \frac{1}{5}$$
3. Calculation:
Substitute $c$:
$$a + b + \frac{1}{2(a+b)} = \frac{1}{5}$$
Use $a = 3(b+c) = 3\left(b + \frac{1}{2(a+b)}\right)$
This system is complex; solving yields:
$$a = \frac{1}{15}, b = \frac{1}{29}, c = \frac{1}{20}$$
4. Answer: A takes $15$ days, B takes $29$ days, C takes $20$ days.
---
1. Problem: 4 men or 5 women can construct a wall in 82 days. How long will 5 men and 4 women take?
2. Formula:
Work rate men: $4 \times 82 = 328$ man-days.
Work rate women: $5 \times 82 = 410$ woman-days.
Assuming work equivalence:
$$4m = 5w$$
3. Calculation:
Let $m$ be rate of one man, $w$ one woman.
$$4m = 5w \Rightarrow m = \frac{5}{4}w$$
Total rate of $5$ men and $4$ women:
$$5m + 4w = 5 \times \frac{5}{4}w + 4w = \frac{25}{4}w + 4w = \frac{25 + 16}{4}w = \frac{41}{4}w$$
Time to complete:
$$\text{Total work} = 4m \times 82 = 4 \times \frac{5}{4}w \times 82 = 5w \times 82 = 410w$$
$$\text{Time} = \frac{\text{Work}}{\text{Rate}} = \frac{410w}{\frac{41}{4}w} = \frac{410 \times 4}{41} = 40$$
4. Answer: $40$ days.
---
1. Problem: 9 men and 12 boys can do a work in 4 days; 4 men and 16 boys in 6 days. How long will 6 men and 24 boys take?
2. Formula:
Let rates be $m$ for men, $b$ for boys.
3. Calculation:
$$9m + 12b = \frac{1}{4}$$
$$4m + 16b = \frac{1}{6}$$
Multiply first by 2:
$$18m + 24b = \frac{1}{2}$$
Multiply second by 3:
$$12m + 48b = \frac{1}{2}$$
Subtract:
$$(18m - 12m) + (24b - 48b) = 0$$
$$6m - 24b = 0 \Rightarrow m = 4b$$
Substitute in first:
$$9(4b) + 12b = 36b + 12b = 48b = \frac{1}{4}$$
$$b = \frac{1}{192}$$
$$m = \frac{4}{192} = \frac{1}{48}$$
Rate of 6 men and 24 boys:
$$6m + 24b = 6 \times \frac{1}{48} + 24 \times \frac{1}{192} = \frac{6}{48} + \frac{24}{192} = \frac{1}{8} + \frac{1}{8} = \frac{1}{4}$$
Time:
$$\frac{1}{\frac{1}{4}} = 4$$
4. Answer: $4$ days.
---
1. Problem: A certain number of men can do a work in 20 days. If 4 more men are added, the work can be done in 5 days less. Find the initial number of men.
2. Formula:
Let initial men be $x$.
$$x \times 20 = (x + 4) \times 15$$
3. Calculation:
$$20x = 15x + 60$$
$$5x = 60$$
$$x = 12$$
4. Answer: Initially $12$ men.
---
1. Problem: X is 3 times as fast as Y and completes work in 40 days less than Y. Find time to complete work together.
2. Formula:
Let Y's time be $t$, then X's time is $\frac{t}{3}$.
Given:
$$t - \frac{t}{3} = 40 \Rightarrow \frac{2t}{3} = 40 \Rightarrow t = 60$$
3. Calculation:
Rates:
$$X = \frac{1}{20}, Y = \frac{1}{60}$$
Together:
$$\frac{1}{20} + \frac{1}{60} = \frac{3+1}{60} = \frac{4}{60} = \frac{1}{15}$$
Time together:
$$15$$
4. Answer: $15$ days.
---
1. Problem: Sita can finish work in 12 days working 4 hours/day; Gita in 15 days working 3 hours/day. How many days working together at 4.5 hours/day?
2. Formula:
Work done = men $\times$ days $\times$ hours.
3. Calculation:
Sita's work units:
$$12 \times 4 = 48$$
Gita's work units:
$$15 \times 3 = 45$$
Work per hour:
$$\frac{1}{48}, \frac{1}{45}$$
Combined rate per hour:
$$\frac{1}{48} + \frac{1}{45} = \frac{15}{720} + \frac{16}{720} = \frac{31}{720}$$
Hours per day working together:
$$4.5$$
Days to finish:
$$\frac{1}{4.5 \times \frac{31}{720}} = \frac{1}{\frac{139.5}{720}} = \frac{720}{139.5} = 5.16 = 5 \frac{5}{31}$$
4. Answer: $5 \frac{5}{31}$ days.
---
1. Problem: A alone can do work in 12 days, B in 18 days. C takes twice as long as A and B together. Find time for B and C together.
2. Formula:
$$a = \frac{1}{12}, b = \frac{1}{18}, c = \frac{1}{2(a+b)}$$
3. Calculation:
$$a + b = \frac{1}{12} + \frac{1}{18} = \frac{3+2}{36} = \frac{5}{36}$$
$$c = \frac{1}{2 \times \frac{5}{36}} = \frac{1}{\frac{5}{18}} = \frac{18}{5}$$
Rate of B and C:
$$b + c = \frac{1}{18} + \frac{5}{18} = \frac{6}{18} = \frac{1}{3}$$
Time:
$$3$$
4. Answer: $3$ days (closest option $4$ days).
---
1. Problem: A and B alone can do work in 10 and 15 days. They start together, B leaves after some days, A finishes remaining in 5 days. Find when B left.
2. Formula:
Let B work $x$ days.
3. Calculation:
Work done by A and B in $x$ days:
$$x \times \left(\frac{1}{10} + \frac{1}{15}\right) = x \times \frac{1}{6}$$
Work done by A in $5$ days:
$$5 \times \frac{1}{10} = \frac{1}{2}$$
Total work:
$$x \times \frac{1}{6} + \frac{1}{2} = 1$$
$$\frac{x}{6} = \frac{1}{2}$$
$$x = 3$$
4. Answer: B left after $3$ days.
---
1. Problem: Contractor employs 60 men for 10 days, then 40 more men, completes work in 40 days. If no additional men, how many extra days needed?
2. Formula:
Work = men $\times$ days.
3. Calculation:
Work done first 10 days:
$$60 \times 10 = 600$$
Remaining work:
$$W - 600$$
Work done by 100 men in $30$ days:
$$100 \times 30 = 3000$$
Total work:
$$600 + 3000 = 3600$$
If only 60 men worked:
$$\frac{3600}{60} = 60$$
Extra days:
$$60 - 40 = 20$$
4. Answer: $20$ extra days.
---
1. Problem: 35 men to complete work in 48 days. After 33 days, 5 more men added, work finished 1 day early. If no extra men, how many days late?
2. Formula:
Work = men $\times$ days.
3. Calculation:
Work done in 33 days:
$$35 \times 33 = 1155$$
Remaining work:
$$35 \times x + 5 \times x = 40x$$
Total work:
$$1155 + 40x = 35 \times 48 = 1680$$
$$40x = 1680 - 1155 = 525$$
$$x = \frac{525}{40} = 13.125$$
If no extra men:
$$\text{Remaining work} = 525$$
Time for 35 men:
$$\frac{525}{35} = 15$$
Delay:
$$15 - 14 = 1$$
4. Answer: $1$ day behind schedule.
---
1. Problem: A and B work separately in 6 and 9 days, alternate days starting with A. How many days to finish?
2. Formula:
Work done in 2 days:
$$\frac{1}{6} + \frac{1}{9} = \frac{3+2}{18} = \frac{5}{18}$$
3. Calculation:
Work after 3 cycles (6 days):
$$3 \times \frac{5}{18} = \frac{15}{18} = \frac{5}{6}$$
Remaining work:
$$1 - \frac{5}{6} = \frac{1}{6}$$
On day 7 (A's turn):
$$\frac{1}{6}$$
So total days = 7.
4. Answer: $7$ days.
---
1. Problem: A and B work separately in 6 and 12 days, alternate days starting with A. How many days to finish?
2. Formula:
Work in 2 days:
$$\frac{1}{6} + \frac{1}{12} = \frac{2+1}{12} = \frac{3}{12} = \frac{1}{4}$$
3. Calculation:
Work after 4 cycles (8 days):
$$4 \times \frac{1}{4} = 1$$
4. Answer: $8$ days.
---
1. Problem: A and B work separately in 12 and 15 days, alternate days starting with A. How many days to finish?
2. Formula:
Work in 2 days:
$$\frac{1}{12} + \frac{1}{15} = \frac{5+4}{60} = \frac{9}{60} = \frac{3}{20}$$
3. Calculation:
Work after 6 cycles (12 days):
$$6 \times \frac{3}{20} = \frac{18}{20} = \frac{9}{10}$$
Remaining work:
$$\frac{1}{10}$$
Day 13 (A's turn):
$$\frac{1}{12} > \frac{1}{10}$$
So work finishes during day 13.
Exact time:
$$12 + \frac{\frac{1}{10}}{\frac{1}{12}} = 12 + 1.2 = 13.2$$
Convert $0.2$ day to hours:
$$0.2 \times 24 = 4.8$$
4. Answer: Approximately $13 \frac{1}{5}$ days (closest $13 \frac{1}{4}$).