Suresh can complete a work in 40 days and Rajesh can complete the same work in 60 days. Find the sequential order of step, in how many days will they complete the work by working together?
(A) Rajesh and Suresh one day's work are `(1)/(60)` and `(1)/(40)`, respectively.
(B) One day's work of both is `(1)/(40)+(1)/(60)`.
(C ) Both can complete the work in 24 days.
(D) One day's work of both `=(1)/(24)`

Options

A. ACDB
B. BCAD
C. CDBA
D. ABDC

Answer

To solve the problem step by step, let's break it down:

### Step 1: Determine the work done by Suresh and Rajesh in one day.
- Suresh can complete the work in 40 days. Therefore, his one day's work is:
\[ \text{One day's work of Suresh} = \frac{1}{40} \]

- Rajesh can complete the work in 60 days. Therefore, his one day's work is:
\[ \text{One day's work of Rajesh} = \frac{1}{60} \]

### Step 2: Calculate the combined work done by Suresh and Rajesh in one day.
- To find the total work done by both in one day, we add their one day's work:
\[ \text{One day's work of both} = \frac{1}{40} + \frac{1}{60} \]

- To add these fractions, we need a common denominator. The least common multiple (LCM) of 40 and 60 is 120. So, we convert the fractions:
\[ \frac{1}{40} = \frac{3}{120} \quad \text{(since } 1 \times 3 = 3 \text{ and } 40 \times 3 = 120\text{)} \]
\[ \frac{1}{60} = \frac{2}{120} \quad \text{(since } 1 \times 2 = 2 \text{ and } 60 \times 2 = 120\text{)} \]

- Now, we can add the two fractions:
\[ \text{One day's work of both} = \frac{3}{120} + \frac{2}{120} = \frac{5}{120} \]

### Step 3: Simplify the combined work.
- We can simplify \(\frac{5}{120}\):
\[ \frac{5}{120} = \frac{1}{24} \]

### Step 4: Calculate the total time taken to complete the work together.
- If their combined work in one day is \(\frac{1}{24}\), then the total time taken to complete the work together is the reciprocal of their combined work:
\[ \text{Total days to complete the work} = \frac{1}{\frac{1}{24}} = 24 \text{ days} \]

### Final Answer:
- Suresh and Rajesh can complete the work together in **24 days**.