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In all level competitive examinations questions on Time and Work have been asked. Due to limited number of types you can ensure your marks with minimum efforts. In these questions, time taken by one/two persons or groups in doing certain works,required number of persons for any work are commonly asked. Comparison of male, female, children works, time taken after distribution/change and questions based on efficiency (per cent of ratio) are also asked.

M = Number of men

D = Number of days

H = Number of hours per day

W = Amount of work

**Relationship between Men and Work.**

More men ==========⇒ can do ==========⇒ More work

Less men ===========⇒ can do =========⇒ Less work

**Relationship between Work and Time**

More work ==========⇒ takes ==========⇒ More Time

Less work ===========⇒ takes ==========⇒ Less Time

** Relationship between Men and Time**

More men ===========⇒ can do in =======⇒ Less Time

Less men ============⇒ can do in =======⇒ More Time

*RULE 1 :* If M1 men can finish W1 work in D1 days and M2 men can finish W2 work in D2 days then, Relation is

If M1 men finish W1 work in D1 days, working T1 timezeach day and M2 men finish W2 work in D2 days, working

T2 time each day, then

RULE 2 : If A completes a piece of work in ‘x’ days,and B completes the same work in ‘y’ days, then

Work done by A in 1 day =1/X, Work done by B in 1 day =1/Y

Work done by A and B in 1 day =

Total time taken to complete the work by A and B both =

RULE 3 : If A can do a work in ‘x’ days, B can do the same work in ‘y’ days, C can do the same work in ‘z’ days

then, total time taken by A, B and C to complete the work together

RULE 4 : If A alone can do a certain work in ‘x’ days and A and B together can do the same work in ‘y’ days,

then B alone can do the same work in

RULE 5 : If A and B can do a work in ‘x’ days, B and C can do the same work in ‘y’ days, C and A can do the same

work in ‘z’ days. Then total time taken, when A, B and C work together =

RULE 6 : Work of one day =Total work/Total no.of working days

Total work = (work of one day) × (total no. of working days)

Remaining work = 1 – (work done)

Work done by A = (Work done in 1 day by A) × (total no.of days worked by A

RULE 7 : If A can finish m/n part of the work in D days.Then,Total time taken to finish the work by A =

RULE 8 :

(i) If A can do a work in ‘x’ days and B can do the same work in ‘y’ days and when they started working

together, B left the work ‘m’ days before completion then total time taken to complete work is

(ii) A leaves the work ‘m’ days before its completion then total time taken to complete work is

RULE 9 : If A and B together can finish a certain work in ‘a’ days. They worked together for ‘b’ days and then ‘B’

(or A) left the work. A (or B) finished the rest work in ‘d’ days, then,Total time taken by A (or B) alone to complete the work

RULE 10 : If food is available for ‘a’ days for ‘A’ men at a certain place and after ‘b’ days. ‘B’ men join, then the

remaining food will serve total men for Required time =

**Example:-**

A and B can do a work in 12 days, B and C in 15 days and C and A in 20 days. If A, B and C work together, they will complete the work in

**solution:-Using Rule 5, Time taken**

**Example:-**

A can do a work in 6 days and B in 9 days. How many days will both take together to complete the work?

**solution:-**Using Rule 2,

**Practice Problems On Time and Work**

**Practice Problems On Time and Work**

**Q1: A, B and C can do a work in 6, 8 and 12 days respectively. Doing that work together they get an amount of Rs. 1350. What is the share of B in that amount?**

**Shortcut trick:** A’s share : B’s share : C’s share =

*B’s time * C’s time : A’s time * C’s time : A’s time * B’s time*

*= 96 : 72 : 48 = 4 : 3 : 2*

*B’s share = 1350/9 * 3*

*= 450 Rs.*

**Q2: A is 20% more efficient than B and 50% more efficient than C. if they together can do a work in 24 days then find in how many days B alone can do the work?**

*A) 60days*

*B) 72days*

*C) 90days*

*D) 180days*

*E) 100days*

*View Answer : Option B*

Solution:

*. A ………B | A………C*

*Efficiency 6……….5 | 3………2*

*Days 5……….6 | 2………3*

*Days A : B : C*

*. 10 12 15*

*A = 10……….6*

*B = 12………..5 …. (LCM = 60)*

*C = 15………..4*

*A+B+ C = 15*

*60/15=4*

*4=24*

*1= 6*

*B=12= 12*6 = 72days*

**Q3: A can a work in 50 days and B is 50% efficient than A. find in how many days A and B together can complete the work?**

*A) 30*

*B) 40*

*C) 50*

*D) 33(1/3)*

*E) 16(2/3)*

*View Answer : Option D*

Solution: B is 50% efficient than A

*. A………..B*

*Efficiency 2……….. 1*

*Days 1…………2*

*1 == 50 . So 2 == 100*

*A= 50……….2 (LCM = 100)*

*B =100………1*

*A+ B = 3*

*100/3 =33(1/3) days.*

**Q4: 30 men are supposed to do a work in 38 days. After 25 days, 5 more men were employed on work for which the work is completed in 1 day before . If 5 more men were not worked then how many days took in delay?
**A) 1 day

*B) 2 days*

*C) 3 days*

*D) 4 days*

*E) None of these.*

*View Answer : Option A*

**Solution:****30Men * 25 days = 750***35 Men * 12 Days = 420*

*Total =750+420=1170*

*Now,1170/30 =39 days*

*1 day delay*

**Q5: A group of men decided to do a job in 4 days but 20 men dropped out everyday ,the job was completed at the end of the 7th day .Find the men who are in the work initially ?**

*A) 155*

*B) 135*

*C) 120*

*D) 140*

*E) 160*

*View Answer : Option D*

**Solution:***Total work = M * 4 = 4M*

*M + (M+20) +…….*

*7/2 [2M +6(-20)] =4M*

*M=140*

**Q6: Ram and Ritesh can do a piece of work in 24 and 30 days respectively. They both started and worked for 6 days. Ritesh then leaves the work and another their friend Ronie joins the work and completed the remaining work with Ram in 11 days . Find how many days are taken by Ronie alone to finish the work?
**A) 110 days

*B) 132 days*

*C) 150 days*

*D) 120 days*

*E) None of these.*

*View Answer : Option D*

**Solution:***(1/24 + 1/30) *6 +(1/24 + 1/Ronie ) *11 = 1*

*Therefore ,Ronie takes 120 days to finish the work.*

**Q7: A tap take 42hrs extra to fill a tank due to a leakage equivalent to half of its inflow. The inlet pipe alone can fill the tank in how many hour?**

*A) *42hr*s*

*B) 21hrs*

*C) 36hrs*

*D) 28hrs*

*E) 30hrs*

*View Answer : Option A*

Solution:

*.Without leak……………………With leak*

*Efficiency 2………………………….1*

*Time 1…………………………..2*

*. +1 == 42hours*

*So 42hours*

**Q8: A can write 75 pages in 25 hrs. A and B together can write 135 pages in 27 hrs. In what time can B write 42 pages?**

*A) 17*

*B) 19*

*C) 23*

*D) 21*

*E) 20*

*View Answer : Option D*

Solution:

*A can write 75/25 =3pages in 1hr*

*A+B can 135/27 = 5pages in 1hr*

*B can write 5-3 = 2page in 1hr*

*42/2 =21hrs*

**Q9: A & B can do a piece of work in 80days. B & C can do same work in 50 days and C & A can do same work in 60 days. Find in how many days they all together can complete that work?**

*A) 40 (40/59)*

*B) 60 (40/59)*

*C) 36 (40/59)*

*D) 25 (40/59)*

*E) 26 (40/59)*

*View Answer : Option A*

Solution:

*LCM = 2400*

*A + B = 80………….2400/80 = 30*

*B + C = 50…………………………..48*

*C + A = 60…………………………..40*

*2(A + B + C) = 118*

*A+ B + C = 59*

*So 2400/59 days*

**Q10: A & B separately can do a piece of work in 9days and 12days respectively. If they work for a day alternatively, A starts the work, in how many days will the work will get completed?
**A) 12(1/4)

*B) 10(1/4)*

*C) 8(1/6)*

*D) 10(5/6)*

*E) 9(1/6)*

*View Answer : Option B*

Solution:

*A=9 4*

*B=12 3 [LCM=36]*

*2 days alternate (4+3) = 7 days*

*2*5 7*5*

*10days 35days*

*now A’s turn so- 10(1*/4

*) days*

**Q11: A and B together can complete a work in 30days and B alone can do it in 60days. Find in how many days A alone can do the work?**

*A) 40*

*B) 60*

*C) 120*

*D) 90*

*E) 110*

*View Answer Option B*

Solution:

*A+B…30……2*

*B……60……*

__1__……………(LCM=60)*A ……………1*

*A = 60/1 = 60*

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