A man spends $\frac{1}{3}$ of his salary on rent and \(\frac... | Mathematics MCQ | Examoogle

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MathematicsArithmetic

A man spends $\frac{1}{3}$ of his salary on rent and $\frac{1}{5}$ on food. If the salary is ₹30,000, then how much remains?

14,000

16,000

18,000

20,000

Correct Answer

⚙️ TE • Technical Direct Fractional SubtractionMathematicsArithmetic

Option A

14,000

Quick Summary:

Calculate the total spent fraction as $\frac{1}{3} + \frac{1}{5} = \frac{8}{15}$ . The remaining fraction is $1 - \frac{8}{15} = \frac{7}{15}$ . Now, calculate $\frac{7}{15} \times 30,000 = 7 \times 2,000 = 14,000$ .

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📐MAMath SolutionDirect Fractional Subtraction

📋 Given

Total salary = 30,000, fraction spent on rent = 1/3, fraction spent on food = 1/5

🔢 Formula Used

R=S×(1−(13+15))R = S \times \left( 1 - (\frac{1}{3} + \frac{1}{5}) \right)R=S×(1−(31​+51​))

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Many students calculate $\frac{1}{3}$ of 30,000 and $\frac{1}{5}$ of 30,000 separately and subtract, but errors occur in arithmetic if fractions are complex; always simplify the fractions first.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total fraction spent

Add the two fractions representing expenses: $\frac{1}{3} + \frac{1}{5}$ . Using a common denominator of 15, we get $\frac{5+3}{15} = \frac{8}{15}$ .

13+15=515+315=815\frac{1}{3} + \frac{1}{5} = \frac{5}{15} + \frac{3}{15} = \frac{8}{15}31​+51​=155​+153​=158​

Determine the remaining fraction

Subtract the total spent fraction from the whole (1) to find the remaining portion of the salary.

1−815=15−815=7151 - \frac{8}{15} = \frac{15-8}{15} = \frac{7}{15}1−158​=1515−8​=157​

Calculate the remaining amount

Multiply the remaining fraction by the total salary of 30,000.

Remaining Amount=715×30,000=7×2,000=14,000\text{Remaining Amount} = \frac{7}{15} \times 30,000 = 7 \times 2,000 = 14,000Remaining Amount=157​×30,000=7×2,000=14,000

✅

A is correct because the remaining fraction of the salary is 7/15, which results in ₹14,000 when multiplied by the total salary of ₹30,000.

Core Concepts Used

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Fractional arithmetic Common denominators Remainder principles

💡 EXAM TIP

This concept is fundamental for Data Interpretation questions where multiple expenses are given as percentages or fractions of a total budget.

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