Question

ATTENTION Please.....!!
Solve it as fast as you can......!!



A can complete a work in 10 days, B in 12 days and C in 15 days. All of them began the work together, but A had to leave the work after 2 days of the start and B, 3 days before the completion of the work. How long did the work last?​

Answer 1

Answer:

7 days

Step-by-step explanation:

Method - 1 :

A can complete the work in 10 days.

Work done by A in 1 day = (1/10)

B can complete the work in 12 days.

Work done by B in 1 day = (1/12).

C can complete the work in 15 days.

Work done by C in 1 day = 1/15.

Amount of work done by them in 1 day,

=> (1/10) + (1/12) + (1/15)

=> 15/60

=> 1/4

Let the work last for 'x' days.

Given, A had to leave the work after 2 days of the start and B, 3 days before the completion of the work.

A's 2 day work + B's(x - 3) day work + C's x day work = 1

=> 2 * (1/10) + (1/12) * (x - 3) + (1/15) * x = 1

=> (1/5) + (x - 3)/12 + (x/15) = 1

=> (x - 3)/12 + x/15 = 4/5

=> 5(x - 3) + 4x = 48

=> 5x - 15 + 4x = 48

=> 9x = 63

=> x = 7

∴ Work will last for 7 days.

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Method - 2:

Work done by A in 1 - day = 1/10.

Work done by B in 1 - day = 1/12

Work done by C in 1 - day = 1/15

Here,

Initially 3 of them work together for 2 days. One of them leaves after working for 'x' days and at last C remains work for 3 days.

So,

2(1/10 + 1/12 + 1/15) + x(1/12 + 1/15) + 3(1/15) = 1

=> (2/10 + 2/12 + 2/15) + x(1/12 + 1/15) + (3/5) = 1

=> x(1/12 + 1/15) = 3/10

=> x(3/20) = 3/10

=> x = 2

Hence,

So, the total number of days required to complete the whole job as per the constraints set in the question = 2 + 3 + 2 = 7 days.

∴ Work will last for 7 days.

Hope it helps!

Answer 2

Wishing you a happy and safe Holi dear !!! :)