If the `(2)/(7)` th part of a certain sum was donated and `(1)/(4)` th was spent on education, then the balance amount will be

Options

A. `(13)/(28)`
B. `(11)/(28)`
C. `(5)/(28)`
D. `(14)/(28)`

Answer

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

1. **Assume a Total Amount**: Let's assume the total amount is 1 unit.

2. **Calculate the Amount Donated**: The amount donated is given as \(\frac{2}{7}\) of the total amount.
\[ \text{Amount Donated} = \frac{2}{7} \times 1 = \frac{2}{7} \text{ units} \]

3. **Calculate the Amount Spent on Education**: The amount spent on education is given as \(\frac{1}{4}\) of the total amount.
\[ \text{Amount Spent on Education} = \frac{1}{4} \times 1 = \frac{1}{4} \text{ units} \]

4. **Calculate the Total Amount Spent**: Now, we need to find the total amount spent, which is the sum of the amount donated and the amount spent on education.
\[ \text{Total Amount Spent} = \text{Amount Donated} + \text{Amount Spent on Education} = \frac{2}{7} + \frac{1}{4} \]

5. **Find a Common Denominator**: To add \(\frac{2}{7}\) and \(\frac{1}{4}\), we need a common denominator. The least common multiple of 7 and 4 is 28.
- Convert \(\frac{2}{7}\) to a fraction with a denominator of 28:
\[ \frac{2}{7} = \frac{2 \times 4}{7 \times 4} = \frac{8}{28} \]
- Convert \(\frac{1}{4}\) to a fraction with a denominator of 28:
\[ \frac{1}{4} = \frac{1 \times 7}{4 \times 7} = \frac{7}{28} \]

6. **Add the Fractions**: Now we can add the two fractions:
\[ \text{Total Amount Spent} = \frac{8}{28} + \frac{7}{28} = \frac{15}{28} \]

7. **Calculate the Balance Amount**: The balance amount is the total amount minus the total amount spent.
\[ \text{Balance Amount} = 1 - \text{Total Amount Spent} = 1 - \frac{15}{28} \]
- Convert 1 to a fraction with a denominator of 28:
\[ 1 = \frac{28}{28} \]
- Now subtract:
\[ \text{Balance Amount} = \frac{28}{28} - \frac{15}{28} = \frac{28 - 15}{28} = \frac{13}{28} \]

8. **Final Answer**: The balance amount will be \(\frac{13}{28}\) units.