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
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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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