a and b together can do a piece of work in16 days.b and c can do same work in 32 days.after a worked for 4 days and b for 12 days c takes it up and finishes it in 48 days.in how many days will each of them complete work
1/a + 1/b = 1/16
1/b + 1/c = 1/32
4/a + 12/b + 48/c = 1
a can do the job in 160/7 days
b can do the job in 160/3 days
c can do the job in 80 days.
Check:
a can do 7/160 jobs in 1 day, and 28/160 jobs in 4 days
b can do 3/160 jobs in 1 day, and 36/160 jobs in 12 days
c can do 1/80 job in 1 day, and 48/80 jobs in 48 days
7/160 + 3/160 = 10/160 = 1/16 so a&b take 16 days
3/160+1/80 = 5/160 = 1/32 so b&c take 32 days
28/160 + 36/160 + 48/80 = 1, as expected.
To solve this question, we can use the concept of work done per day. Let's assume that the work to be done is represented by the unit "W."
Let's first find the individual work rates of each person per day:
Let's say that a does a units of work per day.
Similarly, b does b units and c does c units of work per day.
From the given information, we know:
a + b can complete the work in 16 days, so their combined work rate is equal to W/16.
b + c can complete the work in 32 days, so their combined work rate is equal to W/32.
We also know that after a worked for 4 days and b worked for 12 days, c finished the remaining work in 48 days. So, we can calculate the total work done by each person over these periods.
a worked for 4 days, so the work done by a is 4a units (as a does "a" units per day).
b worked for 12 days, so the work done by b is 12b units (as b does "b" units per day).
c finished the remaining work in 48 days, so the work done by c is c * 48 units.
Now, if we add these three work amounts, it should equal the total work, W. So we have:
4a + 12b + 48c = W
We also know that a + b can complete the work in 16 days, which means their combined work rate is W/16. Similarly, b + c can complete the work in 32 days with a combined work rate of W/32.
Now, let's set up the equations:
(a + b) * 16 = W -- equation 1 (work rate of a + b)
(b + c) * 32 = W -- equation 2 (work rate of b + c)
4a + 12b + 48c = W -- equation 3 (total work done by a, b, and c)
We have three equations and three unknowns. We can solve them simultaneously to find the values of a, b, and c, which will help us determine how many days each person will take to complete the work.