Rakesh can do a piece of work in 20 hours. After he works at it for 8 hours, how much part of the work would be left?

Options

A. `3//5`
B. `5//3`
C. `2//3`
D. `1//5`

Answer

To solve the problem step by step, we can follow these instructions:

### Step 1: Determine Rakesh's work rate
Rakesh can complete the entire work in 20 hours. Therefore, in one hour, he can complete:
\[ \text{Work done in 1 hour} = \frac{1}{20} \]

**Hint:** To find the work done in one hour, divide the total work (1 complete work) by the total time taken (20 hours).

### Step 2: Calculate the work done in 8 hours
If Rakesh works for 8 hours, the amount of work he completes is:
\[ \text{Work done in 8 hours} = 8 \times \frac{1}{20} = \frac{8}{20} = \frac{2}{5} \]

**Hint:** Multiply the work done in one hour by the number of hours worked to find the total work done.

### Step 3: Calculate the remaining work
To find out how much work is left after Rakesh has worked for 8 hours, we subtract the work done from the total work:
\[ \text{Remaining work} = 1 - \text{Work done in 8 hours} = 1 - \frac{2}{5} \]
To perform this subtraction, convert 1 into a fraction with a common denominator:
\[ 1 = \frac{5}{5} \]
So,
\[ \text{Remaining work} = \frac{5}{5} - \frac{2}{5} = \frac{3}{5} \]

**Hint:** To find the remaining work, subtract the fraction of work done from the total work (which is 1, represented as \(\frac{5}{5}\)).

### Conclusion
The part of the work that would be left after Rakesh works for 8 hours is:
\[ \frac{3}{5} \]

Thus, the answer is option A: \( \frac{3}{5} \).