1) **If 9 men working 6 hours a day can do a work in 88 days. Then 6 men working 8 hours a day can do it in how many days?**

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)

so (9*6*88/1) = (6*8*d/1)

on solving, d = 99 days.

**2) If 34 men completed 2/5th of a work in 8 days working 9 hours a day. How many more man should be engaged to finish the rest of the work in 6 days working 9 hours a day?**

Solution: From the above formula i.e (m1*t1/w1) = (m2*t2/w2)

so, (34*8*9/(2/5)) = (x*6*9/(3/5))

so x = 136 men

number of men to be added to finish the work = 136-34 = 102 men

**3) If 5 women or 8 girls can do a work in 84 days. In how many days can 10 women and 5 girls can do the same work?**

Solution: Given that 5 women is equal to 8 girls to complete a work

so, 10 women = 16 girls.

Therefore 10women +5girls = 16girls+5girls = 21 girls.

8 girls can do a work in 84 days

then 21 girls ————— ?

Answer = (8*84/21) = 32 days. Therefore 10 women and 5 girls can a work in 32 days

**4) Worker A takes 8 hours to do a job. Worker B takes 10hours to do the same job. How long it take both A & B, working together but independently, to do the same job?**

Solution: A s one hour work = 1/8.

B s one hour work = 1/10

(A+B) s one hour work = 1/8+1/10 = 9/40

Both A & B can finish the work in 40/9 days

**5) A can finish a work in 18 days and B can do the same work in half the time taken by A. Then, working together, what part of the same work they can finish in a day?**

Solution:Given that B alone can complete the same work in days = half the time

taken by A = 9days

A s one day work = 1/18

B s one day work = 1/9

(A+B) one day work = 1/18+1/9 = 1/6

**6) A is twice as good a workman as B and together they finish a piece of work in 18 days.In how many days will A alone finish the work.**

Solution: if A takes x days to do a work then

B takes 2x days to do the same work

= > 1/x+1/2x = 1/18

= > 3/2x = 1/18

= > x = 27 days.

Hence, A alone can finish the work in 27 days.

**7) A can do a certain work in 12 days. B is 60% more efficient than A. How many days does B alone take to do the same job?**

Solution: Ratio of time taken by A & B = 160:100 = 8:5

Suppose B alone takes x days to do the job.

Then, 8:5::12:x

= > 8x = 5*12

= > x = 15/2 days.

**8) A can do a piece of work n 7 days of 9 hours each and B alone can do it in 6 days of 7 hours each. How long will they take to do it working together 8 2/5 hours a day?**

Solution: A can complete the work in (7*9) = 63 days

B can complete the work in (6*7) = 42 days

= > A s one hours work = 1/63 and

B one hour work = 1/42

(A+B) one hour work = 1/63+1/42 = 5/126

Therefore, Both can finish the work in 126/5 hours.

Number of days of 8 2/5 hours each = (126*5/(5*42)) = 3 days

**9) A takes twice as much time as B or thrice as much time to finish a piece of work. Working together they can finish the work in 2 days. B can do the work alone in ?**

Solution: Suppose A,B and C take x,x/2 and x/3 hours respectively finish the

work then 1/x+2/x+3/x = 1/2

= > 6/x = 1/2

= >x = 12

So, B takes 6 hours to finish the work.

**10) X can do ¼ of a work in 10 days, Y can do 40% of work in 40 days and Z can do 1/3 of work in 13 days. Who will complete the work first?**

Solution: Whole work will be done by X in 10*4 = 40 days.

Whole work will be done by Y in (40*100/40) = 100 days.

Whole work will be done by Z in (13*3) = 39 days

Therefore,Z will complete the work first.

Complex Problems on Time and Work

**1) A and B undertake to do a piece of workfor Rs 600. A alone can do it in 6 days while B alone can do it in 8 days. With the help of C, they can finish it in 3 days, Find the share of each?**

Solution:C one days work = (1/3)-(1/6+1/8) = 1/24

Therefore, A:B:C = Ratio of their one days work = 1/6:1/8:1/24 = 4:3:1

A share = Rs (600*4/8) = 300

B share = Rs (600*3/8) = 225

C share = Rs[600-(300+225)] = Rs 75

**2) A can do a piece of work in 80 days. He works at it for 10 days & then B alone finishes the remaining work in 42 days. In how much time will A and B, working together, finish the work?**

Solution: Work done by A in 10 days = 10/80 = 1/8

Remaining work = (1-(1/8)) = 7/8

Now, work will be done by B in 42 days.

Whole work will be done by B in (42*8/7) = 48 days

Therefore, A one day work = 1/80

B one days work = 1/48

(A+B) one days work = 1/80+1/48 = 8/240 = 1/30

Hence, both will finish the work in 30 days.

**3) P,Q and R are three typists who working simultaneously can type 216 pages in 4 hours In one hour, R can type as many pages more than Q as Q can type more than P. During a period of five hours, R can type as many pages as P can during seven hours. How many pages does each of them type per hour?**

Solution: Let the number of pages typed in one hour by P, Q and R be x,y and z respectively. Then

x+y+z = 216/4 = 54 ————— 1

z-y = y-x = > 2y = x+z ———–— 2

5z = 7x = > x = 5x/7 ————— 3

Solving 1,2 and 3 we get x = 15,y = 18, and z = 21

**4) Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages?**

Solution: Number of pages typed by Ronald in one hour = 32/6 = 16/3

Number of pages typed by Elan in one hour = 40/5 = 8

Number of pages typed by both in one hour = ((16/3)+8) = 40/3

Time taken by both to type 110 pages = 110*3/40 = 8 hours.

**5) Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both working together. If B worked alone, he would need 4 1/2 hours more to compete the job than they both working together. What time would they take to do the work together.**

Solution: (1/(x+8))+(1/(x+(9/2))) = 1/x

= >(1/(x+8))+(2/(2x+9)) = 1/x

= > x(4x+25) = (x+8)(2x+9)

= > 2×2 = 72

= > x2 = 36

= > x = 6

Therefore, A and B together can do the work in 6 days.

**6) A and B can do a work in12 days, B and C in 15 days, C and A in 20 days. If A,B and C work together, they will complete the work in how many days?**

Solution: (A+B)s one days work = 1/12;

(B+C)s one days work = 1/15;

(A+C)one days work = 1/20;

Adding we get 2(A+B+C) one day work = 1/12+1/15+1/20 = 12/60 = 1/5

(A+B+C) one day work = 1/10

So, A,B,and C together can complete the work in 10 days.

**7) A and B can do a work in 8 days, B and C can do the same wor in 12 days. A,B and C together can finish it in 6 days. A and C together will do it in how many days?**

Solution: (A+B+C) one day work = 1/6;

(A+B) one day work = 1/8;

(B+C) one day work = 1/12;

(A+C)one day work = 2(A+B+C) one days work-((A+B) one day

work+(B+C) one day work)

= (2/6)-(1/8+1/12)

= (1/3)- (5/24)

= 3/24

= 1/8

So, A and C together will do the work in 8 days.

**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 how many days?**

Solution: (A+B) one day work = 1/10;

C one day work = 1/50

(A+B+C) one day work = (1/10+1/50) = 6/50 = 3/25

Also, A one day work = (B+C) one day work

From i and ii ,we get :2*(A one day work) = 3/25

= > A one day work = 3/50

B one day work = (1/10-3/50)

= 2/50

= 1/25

B alone could complete the work in 25 days.

**9) A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:**

Solution: Ratio of times taken by A and B = 1:3.

If difference of time is 2 days , B takes 3 days

If difference of time is 60 days, B takes (3*60/2) = 90 days

So, A takes 30 days to do the work = 1/90

A one day work = 1/30;

B one day work = 1/90;

(A+B) one day work = 1/30+1/90 = 4/90 = 2/45

Therefore, A & B together can do the work in 45/2days

**10) A can do a piece of work in 80 days. He works at it for 10 days and then B alone finishes the remaining work in 42 days. In how much time will A & B, working together, finish the work?**

Solution: Work Done by A n 10 days = 10/80 = 1/8

Remaining work = 1-1/8 = 7/8

Now 7/8 work is done by B in 42 days

Whole work will be done by B in 42*8/7 = 48 days

= > A one day work = 1/80 and

B one day work = 1/48

(A+B) one day work = 1/80+1/48 = 8/240 = 1/30

Hence both will finish the work in 30 days.

**11) 45 men can complete a work in 16 days. Six days after they started working, so more men joined them. How many days will they now take to complete the remaining work?**

Solution: M1*D1/W1 = M2*D2/W2

= >45*6/(6/16) = 75*x/(1-(6/16))

= > x = 6 days

**12) A is 50% as efficient as B. C does half the work done by A & B together. If C alone does the work n 40 days, then A,B and C together can do the work in:**

Solution: A one day work:B one days work = 150:100 = 3:2

Let A & B one day work be 3x and 2x days respectively.

Then C one day work = 5x/2

= > 5x/2 = 1/40

= > x = ((1/40)*(2/5)) = 1/100

A one day work = 3/100

B one day work = 1/50

C one day wor

**Sandeep Joshi**

Mathematics, Technology and Programming are my passion. I am a part of Java Ecosystem and through this blog, I contribute to it. I am here to blog about my interests, views and experiences.

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