A B and C can complete a job by themselves in 10 days 15 days in 30 days respectively A and B start the work together but after 2 days B leaves the remaining work is then completed by a and see how long did a and c work together
Answers
Answer:
In 7 days, the total work was completed
Solution:
Given that,
A, B and C can complete a work in 10, 12 and 15 days respectively
Given that,
After 2 days, A leaves the job
So, A worked for 2 days alone
Let "x" be the days in which total work was completed
B left the job 3 days before the work was completed
Therefore,
B worked for (x - 3) days
C completed the remaining work alone
Thus C worked for "x" days
Therefore,
\begin{gathered}\frac{2}{10} + \frac{x-3}{12} + \frac{x}{15} = 1\\\\Make\ the\ denominators\ same\\\\\frac{2 \times 6}{10 \times 6} + \frac{(x-3) \times 5}{12 \times 5} + \frac{x \times 4}{15 \times 4} = 1\\\\12 + 5x - 15 + 4x = 60\\\\9x - 3 = 60\\\\9x = 63\\\\x = 7\end{gathered}
10
2
+
12
x−3
+
15
x
=1
Make the denominators same
10×6
2×6
+
12×5
(x−3)×5
+
15×4
x×4
=1
12+5x−15+4x=60
9x−3=60
9x=63
x=7
Thus, in 7 days, the total work was completed
Answer:
the time till when a and b will work together is 5 days.
