Question

6. 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?
(A) 60 days
(B) 120 days
(C) 110 days (D) 55 days​

Answer 1

Answer:The answer is 110 days.

Step-by-step explanation:

A+b=72-@1

B+C=120-@2

C+A=90-@3

Now you can easy solve it by these equations

Answer 2

Answer:

(B) 120 days

Step-by-step explanation:

Let A take x days, B take y days and C take z days to complete the work alone.

Thus, Work done by A in 1 day = 1/x

Work done by B in 1 day = 1/y

Work done by C in 1 day = 1/z.

Work done by A and B together in one day = 1/x + 1/y

Work done by B and C together in one day = 1/y + 1/z

Work done by A and C together in one day = 1/z + 1/x

Thus, time taken by A and B to together complete the work = $\frac{1}{1/x+1/y}$

Also, time taken by B and C to together complete the work = $\frac{1}{1/y+1/z}$

Also, time taken by C and A to together complete the work = $\frac{1}{1/x+1/z}$

By the given conditions,

$\frac{1}{1/x+1/y}$ = 72

$\frac{1}{1/y+1/z}$ = 120

$\frac{1}{1/x+1/z}$ = 90

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

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

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

Subtracting equation ( 2 ) from equation ( 3 ),

1/x - 1/y = 1/90 - 1/120

or 1/x - 1/y = 1/360 -----------( 4 )

Adding equations ( 1 ) and ( 4 ),

2/x = 1/72 + 1/360

or 2/x = 1/60

or x = 120.

Thus, A can finish the work alone in 120 days.

Option (B) is correct

Hope it helped you.

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