A and B receive same amount of salary. A spends 1^3 on rent, 1^4 on food and 1^5 on education while B spends 1^3 on rent,1^5 on food and 2^5 on education.What fraction of salary is saved by A and B.

Let \( S \) be the salary for both A and B.

### For A:
- Rent: \( \frac{1}{3} \) of the salary
- Food: \( \frac{1}{4} \) of the salary
- Education: \( \frac{1}{5} \) of the salary

The total spending for A is:
\[
\frac{1}{3} + \frac{1}{4} + \frac{1}{5}
\]

To compute this, we need the common denominator of 3, 4, and 5, which is 60. Let's rewrite each fraction with denominator 60:
\[
\frac{1}{3} = \frac{20}{60}, \quad \frac{1}{4} = \frac{15}{60}, \quad \frac{1}{5} = \frac{12}{60}
\]

Now sum them up:
\[
\frac{20}{60} + \frac{15}{60} + \frac{12}{60} = \frac{47}{60}
\]

So A spends \( \frac{47}{60} \) of the salary.

The fraction of the salary A saves is:
\[
1 - \frac{47}{60} = \frac{13}{60}
\]

### For B:
- Rent: \( \frac{1}{3} \) of the salary
- Food: \( \frac{1}{5} \) of the salary
- Education: \( \frac{2}{5} \) of the salary

The total spending for B is:
\[
\frac{1}{3} + \frac{1}{5} + \frac{2}{5}
\]

First, let's rewrite the fractions:
\[
\frac{1}{3} = \frac{5}{15}, \quad \frac{1}{5} = \frac{3}{15}, \quad \frac{2}{5} = \frac{6}{15}
\]

Summing them:
\[
\frac{5}{15} + \frac{3}{15} + \frac{6}{15} = \frac{14}{15}
\]

So B spends \( \frac{14}{15} \) of the salary.

The fraction of the salary B saves is:
\[
1 - \frac{14}{15} = \frac{1}{15}
\]

### Final Answer:
- A saves \( \frac{13}{60} \) of the salary.
- B saves \( \frac{1}{15} \) of the salary.

Would you like further details or have any questions?

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Here are some relative questions to consider:
1. What is the difference in savings between A and B?
2. If the salary were doubled, how would the savings for A and B change?
3. How much more does B spend on education compared to A?
4. What would happen if A or B reduced their spending on rent by half?
5. How can you calculate the percentage of savings for both A and B?

**Tip:** When comparing fractions, finding a common denominator makes it easier to sum or compare them.

A and B receive same amount of salary. A spends 1/3 on rent, 1/4 on food and 1/5 on education while B spends 1/3 on rent, 1/5 on food and 2/5 on education. What fraction of salary is saved by A and B?

Discover how to calculate the savings for A and B based on their spending on rent, food, and education. This problem involves adding and subtracting fractions to determine savings. Suitable for students in Grades 5-7, this example explains the concepts of common denominators and how to compare savings.

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