Three persons A, B and C can paint all the
walls of a house in 4 days when they all
work together. A alone can do it in 15 days.
B alone can do it in 10 days. How long will
C take to do the work alone?
12
Answers
Answer:
A alone can do it in 12 days
In 1 day, A can do = 1/12 of the work
C alone can do it in 10 days
In 1 day, C can do = 1/10 of the work
Let's say B takes b days to finish it.
In 1 day, B can do = 1/b of the work
All of them together can finish it in 4 days
{So in 1 day, they all can do = 1/4 of the work\begin{gathered}\Rightarrow \frac{1}{12} + \frac{1}{10} + \frac{1}{b} = \frac{1}{4} \\ \\ \Rightarrow \frac{1}{b} = \frac{1}{4} - \frac{1}{12} - \frac{1}{10} \\ \\ \Rightarrow \frac{1}{b} = \frac{1 \times 15 - 1 \times 5 - 1 \times 6}{60} \\ \\ \Rightarrow \frac{1}{b} = \frac{ 15 - 5 - 6}{60} \\ \\ \Rightarrow \frac{1}{b} = \frac{4}{60} = \frac{1}{15} \\ \\ \Rightarrow b = 15 \: days\end{gathered}
⇒
12
1
+
10
1
+
b
1
=
4
1
⇒
b
1
=
4
1
−
12
1
−
10
1
⇒
b
1
=
60
1×15−1×5−1×6
⇒
b
1
=
60
15−5−6
⇒
b
1
=
60
4
=
15
1
⇒b=15days
B can do the work alone in 15 days.
he could take five days to complete