Question

Raghav can do a work in 15 days and Akshay in 20 days. If they work on it together for 4 days, then the fraction of the work that is left is :

• A. $\frac{3}{4}$
• B. $\frac{3}{10}$
• C. $\frac{8}{15}$
• D. $\frac{11}{20}$

Hint:

Using the total units of work method makes this simpler:
Let total work be $60 \text{ units}$ (LCM of $15$ and $20$).
- Raghav's rate $= 4 \text{ units/day}$.
- Akshay's rate $= 3 \text{ units/day}$.
Together they do $= 4 + 3 = 7 \text{ units/day}$.
In 4 days they complete $= 4 \times 7 = 28 \text{ units}$.
Remaining work $= 60 - 28 = 32 \text{ units}$.
Fraction left $= \frac{32}{60} = \frac{8}{15}$.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This is a standard time and work problem.
Two individuals are working on the same task with different rates.
We are asked to find the fraction of total work that remains incomplete after both have worked together for a specified number of days.

Step 2: Key Formula or Approach:
Let the total work be represented as $1$ unit.
1. Raghav's 1-day work $= \frac{1}{15}$.
2. Akshay's 1-day work $= \frac{1}{20}$.
3. Combined 1-day work $= \frac{1}{15} + \frac{1}{20}$.
4. Work done in 4 days $= 4 \times (\text{Combined 1-day work})$.
5. Remaining work $= 1 - (\text{Work completed})$.

Step 3: Detailed Explanation:

• Calculate Combined 1-day Work:
\[ \text{Combined 1-day work} = \frac{1}{15} + \frac{1}{20} \] Find the LCM of $15$ and $20$, which is $60$:
\[ \text{Combined 1-day work} = \frac{4 + 3}{60} = \frac{7}{60} \]

• Calculate Work Done in 4 days:
Both work together for 4 days:
\[ \text{Work done in 4 days} = 4 \times \frac{7}{60} = \frac{7}{15} \]

• Calculate the Remaining Work:
The fraction of work left is:
\[ \text{Work left} = 1 - \frac{7}{15} = \frac{15 - 7}{15} = \frac{8}{15} \]

Step 4: Final Answer:
The fraction of the work that is left is $\frac{8}{15}$.
Hence, the correct option is (C).