Question

A+b, B+c do a work in 12 and 16 days
if A work for 5 days and B work for 7 days
and c complete the remaining work in 13 days.
Then find c would complete the work in how
many days ?​

Answer 1

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.