A and B together can do a piece of work in 10 days. If A alone can do the work in 15 days, find in how many days that B alone can do the same work. The following are the steps involved in solving the above problem. Arrange them in sequential order.
One day's work of B is `(1)/(10)-(1)/(5)`.
One day's work of A and B is `(1)/(10)` and one day's work of A is `(1)/(15)`.
B alone can do the work in 30 days.
One day's work of B is `(1)/(30)`.

Options

A. BADC
B. BDAC
C. BCAD
D. ABDC

Explanation

To solve the problem step by step, we can follow this sequence:

1. **Calculate the work done by A and B together in one day.**
Since A and B together can complete the work in 10 days, their combined work in one day is:
\[ \text{One day's work of A and B} = \frac{1}{10} \]

2. **Calculate the work done by A in one day.**
A alone can complete the work in 15 days, so A's work in one day is:
\[ \text{One day's work of A} = \frac{1}{15} \]

3. **Determine the work done by B in one day.**
To find B's work in one day, we subtract A's work from the combined work:
\[ \text{One day's work of B} = \text{One day's work of A and B} - \text{One day's work of A} \]
\[ \text{One day's work of B} = \frac{1}{10} - \frac{1}{15} \]
To perform this subtraction, we need a common denominator, which is 30:
\[ \text{One day's work of B} = \frac{3}{30} - \frac{2}{30} = \frac{1}{30} \]

4. **Calculate the number of days B alone will take to complete the work.**
If B can do \(\frac{1}{30}\) of the work in one day, then B alone can complete the entire work in:
\[ \text{Days taken by B} = \frac{1}{\text{One day's work of B}} = \frac{1}{\frac{1}{30}} = 30 \text{ days} \]

Thus, B alone can do the work in **30 days**.