Answer:

The whole work will be completed in 6.33 DAYS.

Explanation:

A's one day work = 1/15

B's one day work = 1/12

C's one day work = 1/10

(A+B+C)'s one day work = 1/15 + 1/12 + 1/10

= 4 + 5 + 6 / 60

= 15/60 = 1/4

(A+B+C)'s two day work = 1/4 × 2 = 1/2.

By condition,

C left the JOB in two days.

Hence, REMAINING work = 1 - 1/2 = 1/2

Let the whole work be done in x days.

(A+B)'s one day work = 1/15 + 1/12

= 4+5 / 60

= 9/60 = 3/20

(A+B)'s x-3 day work = 3/20 × x-3

= 3x - 9 / 20

Remaining work = 1/2 - 3x-9/20

= 10 - (3x-9) / 20

= 10 - 3x + 9 / 20

= 19 - 3x / 20

Time taken by A to complete the remaining work = 19 - 3x / 20 × 15 = 19 - 3x / 4 × 3

= 3(19 - 3x) / 4 = 57 - 9x / 4

By condition,

1/2 + (3x - 9 / 20) + (57 - 9x / 4) = 1

=> (3x - 9 / 20) + (57 - 9x / 4) = 1 - 1/2

=> (3x - 9) + 5(57 - 9x) / 20 = 1/2

=> 3x - 9 + 285 - 45x / 20 = 1/2

=> 3x - 45x + 285 - 9 / 20 = 1/2

=> - 42x + 276 = 1/2 × 20 = 10

=> - 42x = 10 - 276 = - 266

=> 42x = 266 => x = 266/42 = 6.33 (ans).

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