# A and B can do a piece of work in 72 days B and C in 120 days and A and C in 90 days in what time can A alone do it ​

Math

## Question

A and B can do a piece of work in 72 days B and C in 120 days and A and C in 90 days in what time can A alone do it ​

• ### 1. User Answers omkumar72

B and C takes 120 days

A and C takes 90 days

No.of days taken by B,C and A,C all together =120+90

=210 days

A and B does the work in 72 days

number of days taken C by working two times =210- 72

=138

number of days taken by C =138÷2

=69

number of days taken by A and C together =90

number of days taken by A=90-69

=21

Step-by-step explanation:

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

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

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

adding all three , 2(A+B+C)'s 1 day work =1/72+1/120+1/90

=5+3+4/360

=12/360

=1/30

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

Now ,A's one day work =(A+B+C)'s 1 day work - (B+C)'s 1 day work

=1/60-1/120=2-1/120

=1/120

Hence , A can complete the work in 120 days.

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