TIME AND WORK SOLVED QUESTIONS

Important notes

*If A can do s piece of work in 𝓧 days,then A'S 1 day's work =1/𝓧
Conversely,If A's 1 day's work =1/𝓧,then A can finish the work in 𝓧 days.

*If A can do a piece of work 𝓧 days and B can do it 𝓨 days,then the part of the work finished in 1 day when they work together =1/𝓧+1/𝓨=𝓧+𝓨/𝓧𝓨

So. They will finish the whole work in 𝓧𝓨/𝓧+𝓨

*If M1 persons can do W1 work in D1 days and M2 person can do W2 work in D2 days,then M1D1W2=M2D2W1.In the case of same amount of work W1 =W2 and then M1D1=M2D2.

Solved Questions

1.Ramesh and Suresh can do a job alone in 20 days and 30 days respectivelyIn how many days the job will be finsihed if they work together?

(Ramesh+Suresh)'S 1 day;s work=1/20+1/30=(30+20)/20𝗑30

=1/12 ... So they will finish the job in 12/1= 12 days.

2.A and B together can complete a piece of work in 35 days while A  alone can complete the same work in 60 days.B alone will be able to complete the same work in............days?

(A+B)'S 1 days work=1/35

ie ..A'S 1 days work=1/60

So B'S  1 days work =[1/35−1/60]=5/420=1/84

Hence B alone will finish the work in 84 days.


3.A and B can do a piece of work in 3 days;B and C can do it in 4  days;A and C can do it in 6 days;In how many days can they do it all working together?

(A+B)'S  1 days work =1/3

(B+C)'S  1 days work =1/4

(A+C)'S  1 days work=1/6

So 2(A+B+C)'S  1 days work

=[1/3+1/4+1/6]=9/12=3/4

SO  (A+B+C)'S 1 days work =3/4𝗑1/2=3/8

Hence all working together can do the work in 8/2=2(2/3)days.


4.20 persons can complete a job in 20 days.How many days will 25 men take to complete the same job?

M1=20,  D1 =20  ,M2 =25 .D2= ?

We know M1D1=M2D2

ie 20𝗑20=25𝗑d2

⇒D2=20𝗑20/25=16


5.A does 4/5 of a piece of work in 20 days,he then calls B and they complete the remaining work in 3 days .How long will  B along take to do the whole work?
A)37(1/2) days
B)37 days
C)40 days
D)23 days

Solution

A will do the whole work in 20𝗑5/4 =25 days

so A's one days work=1/25.

Suppose B will complete the whole work in 𝓧 days .Then B's one day's work =1/𝓧

(A+B)'s one  days work=1/25+1/𝓧

Remaining work 1−4/5=1/5

So   (1/25+1/𝓧)𝗑3 days.=1/5

1/25+1/𝓧=1/15

⇒1/𝓧=2/75

⇒𝓧=75/2

=37𝗑1/2

Aswer:A


6.A and B can do a piece of work in 20 days,B and C can do it 15 days, and Aand C can do it in 12 days.How many days will C along take to complete the work?
A)60
B)6
C)30
D)20

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

(B+C)=1/15
and

(A+C)=1/12

⇒2𝗑(A+B+C)'s one day's work

⇒1/20+1/15+1/12=1/5

ie  (A+B+C)'s  one days work =1∕2𝗑3 =1/10

so C's 1 day's work =(A+B+C)'s  1 days work −(A+B)'s  one days work

=1/10−1/20=1/20

Hence C alone will do the work in 20 days.

Answer:A


7.A can complete 1/3 of a work in 5 days and B 2/5 of the work in 10 days.In many days both A and B together can complete the work?
A)10
B)9  (3/8)
C)8  (4/5)
D)7 (1/2)

A can complete the whole work in 5𝗑3/1=15 days

and B  in 10𝗑5/2=25 days

so A's one days work=1/15 and B's one day's work =1/25

ie (A+B) will complete the whole work in 25𝗑15∕25+15=75/8

⇒9(3/8)

Answer:B

Solved Maths Questions