Question : A alone can paint a house in 35 days and B alone can do it in 70 days. Along with C, they did the job in 10 days only. In how many days C alone can do the job?
Option 1: 40 days
Option 2: $\frac{70}{3}$ days
Option 3: $\frac{70}{4}$ days
Option 4: 20 days
Correct Answer: $\frac{70}{4}$ days
Solution :
Given,
A alone can paint a house in 35 days
⇒ A's one day work = $\frac{1}{35}$
Also, B alone can do it in 70 days
⇒ B's one day work = $\frac{1}{70}$
Let C alone can finish the work in $x$ days
According to the question,
⇒ $\frac{1}{35}+\frac{1}{70}+\frac1x=\frac{1}{10}$
⇒ $\frac{2x+x+70}{70x}=\frac{1}{10}$
⇒ $(3x+70)\times10=70x$
⇒ $30x+700=70x$
⇒ $40x=700$
⇒ $x=\frac{70}{4}$
Hence, the correct answer is $\frac{70}{4}$ days.
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