Question

A can finish a work in 8 days, B in 10 days and C in 12 days. I how

many days will they finish it, working all together?​

Answer 1

A and B do (1/8)th of the work in a day.

B and C do (1/12)th of the work in a day.

A and C do (1/16)th of the work in a day.

2A, 2B and 2C do (1/8)+(1/12)+(1/16) = (18/144)+(12/144)+(9/144) = (39/144) or (13/48)th of the work in a day.

Or A, B and C do (13/96)th of the work in a day.

So A, B and C together will complete the whole work in 96/13 or 7 and 5/13th of the 8th day.

Answer 2

Answer:

answer is above

Step-by-step explanation:

24 Days

Let us say that A takes 'a' days to finish the work, B takes 'b' days to finish the work and C takes 'c' days to finish the work.

=> A in one day will do 1/a units of work, and similarly B and C will do 1/b and 1/c units of work in one day.

We are given that A and B together can finish the work in 12 days

=> 1/a + 1/b = 1/12

Similarly, we are also given that B and C together can finish the work in 16 days

=> 1/b + 1/c = 1/16

We also know that the work can be finished if A works for 5 days, B for 7 Days and C for 13 days

=> 5/a + 7/b + 13/c = 1

So, we have three equations and three variables. We can solve them to get the individual values of 'a', 'b' and 'c'. We are asked to find out in how many days would C alone finish the work. So, we are asked to find out the value of 'c'.

If we multiply the first equation with 5 and the second equation with 2 and add them up, we will get

5(1/a + 1/b) + 2(1/b + 1/c) = 5/12 + 2/16

=> 5/a + 7/b + 2/c = (20 + 6)/48 = 26/48

=> 5/a + 7/b + 2/c = 13/24

If we subtract the above equation from the third equation, we will get

(5/a + 7/b + 13/c) - (5/a + 7/b + 2/c) = 1 - 13/24

=> 11/c = 11/24

=> c = 24

So, we can say that C alone will take 24 days to complete the work.

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