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 ?​

Answer 1

Answer:

120 days

Step-by-step explanation:

Let A,B and C can do a piece of work in x,y and z days respectively.

So, A's , B's and C's one days work are 1/x,1/y and 1/z respectively.

now,

1/x + 1/y = 1/72 ...(1)

1/y + 1/z = 1/120 ...(2)

1/z + 1/x = 1/90 ...(3)

now, we add eq (1),(2) and (3)

2( 1/x + 1/y + 1/z ) = 5+3+4/360

1/x + 1/y + 1/z = 1/60 ...(4)

on solving eq (4) and (2)

1/x = 1/60 -1/120 = 1/120

Hence, A alone will complete the work in 120 days.

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Answer 2

Answer:

A and B =72

B and C= 120

A and C= 90

LCM of 72,120,90 = 360

then

A and B= 5

BC = 3

C and A = 4

a + b + c = 12/ 2 ( because A,B,C is two time )

ABC =6

BC =3

then A = 3

now

=360/3

= 120

So 120 is answer .

Thanks .