Threeman a b and c complete the work 15 12 and 10 days a b and c starts work together but c left the work after 2 days and b left the work 3 days before the completion of the work howin how much time the whole work will be completed
Answers
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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