Answer :
In 24 days 7 seniors and 5 juniors will finish the work.
Let's define the following variables:
- - x: The number of days it takes for one senior to finish the work alone
- - y: The number of days it takes for one junior to finish the work alone
Given information:
- - 3 seniors or 7 juniors finish the work in 32 days.
We can set up the following equations:
- 3/x = 1/32 (1)
- 7/y = 1/32 (2)
From equation (1), we get:
x = 32/3 = 96
From equation (2), we get:
y = 32/7 = 128/7
Now, we need to find the number of days it takes for 7 seniors and 5 juniors together to finish the work.
Let z be the number of days it takes for 7 seniors and 5 juniors together to finish the work.
We can use the principle of inverse summation of work rates:
(7/x) + (5/y) = 1/z
Substituting the values of x and y, we get:
(7/96) + (5/128) = 1/z
1/z = (7/96) + (35/128)
1/z = (105/1536) + (35/128)
1/z = (3465/12288) + (2730/12288)
1/z = 6195/12288
z = 12288/6195
z = 24 days
Therefore, 7 seniors and 5 juniors together will finish the work in 24 days.
