Question

PLEASE ANSWER THIS QUESTION

A, B and C can complete a piece of work in 25, 30 and 50 days respectively. They started the work together but A and C left 2 days before the completion of the work. In how many days will the work be completed?

(HINT : Consider the number of days as x. A and C worked for (x-2) days

BRAINLIEST QUESTION

Answer 1

Let the total number of days be x

Number of days A, B and C worked together = x - 2

A's one day work = 1/25

B's one day work = 1/30

C's one day work = 1/50


( A + B + C)'s one day work = ( 1/25 + 1/30 + 1/50)

= ( 6 + 5 + 3) / (150)

= ( 14 / 150)

= 7 / 75

( A + B +C)' s ( x - 2) days work = 7 (x - 2) / 75

= ( 7x - 14) /75

Left work to be done by B = 1 - (7x - 14) /75

= ( 75 - 7x + 14) / 75

= ( 89 - 7x) /75

Number of days required to finish the remaining work = 30 × ( 89 - 7x) / 75

= 2 ( 89 - 7x) / 5

= ( 178 - 14x) / 5

Now,

Number of days they worked together + Number of days B worked alone = Total number of days Required to do the work

x - 2 + ( 178 - 14x) /5 = x

=> ( 178 - 14x) /5 = 2

=> 178 - 14x = 10

=> 14x = 168

=> x = 12

Required number of days = 12