Question

Neha can complete a work in 6 days and Ishrat can complete the same work in 4 days. What will be the time taken by them to complete the same work together ?

• A. \(1\frac{2}{5}\) days
• B. 3 days
• C. \(2\frac{2}{5}\) days
• D. 2 days

Hint:

Add daily work: \(1/6 + 1/4 = 5/12\), so time is \(12/5\) days.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
Two people work on the same job at the same time. We need the time they take to finish it together.

Step 2: Key Formula or Approach:
If a person finishes a job in \(n\) days, the person does \(\dfrac{1}{n}\) of the job in one day. Add the daily shares to get the combined daily work.

Step 3: Detailed Explanation:
Neha does \(\dfrac{1}{6}\) per day and Ishrat does \(\dfrac{1}{4}\) per day.
\[ \frac{1}{6} + \frac{1}{4} = \frac{2 + 3}{12} = \frac{5}{12} \]
So together they finish \(\dfrac{5}{12}\) of the work each day.
\[ \text{Time} = \frac{12}{5} = 2\frac{2}{5} \text{ days} \]

Step 4: Check the other options:
\(1\frac{2}{5}\) days would be too fast, because the faster worker alone needs 4 days and the two together cannot be under 2 days. 3 days and 2 days do not equal \(\dfrac{12}{5}\). Only \(2\frac{2}{5}\) days is right.

Final Answer:
They finish the work together in \(2\frac{2}{5}\) days. \[ \boxed{\frac{12}{5} = 2\frac{2}{5} \text{ days}} \]