Question

Ritesh is twice as good as Mitesh. Ritesh takes 30 days less than Mitesh to finish a task. How long will they take to complete the task together?

• A. 10 days
• B. 20 days
• C. 30 days
• D. 60 days

Hint:

“$k$ times as efficient” $\Rightarrow$ time ratio is $1:k$. Use the difference in times to pin down actual times, then add rates.

Answer 1

The Correct Option is B

“Twice as good” $\Rightarrow$ Ritesh’s rate : Mitesh’s rate $=2:1$. Time is inversely proportional to rate.
Let Ritesh take $x$ days, Mitesh $2x$ days. Given $2x-x=30 \Rightarrow x=30$.
Rates: $\dfrac{1}{30}$ and $\dfrac{1}{60}$ work/day. Together: \[ \frac{1}{T}=\frac{1}{30}+\frac{1}{60}=\frac{1}{20}\quad\Longrightarrow\quad T=20\ \text{days}. \] \[ \boxed{20\ \text{days}} \]