If an increase of 10% in prices. The rise in wages is 20% then the real wage has increased by

Option c: Less than 10%. Solution: Let the initial price level be P0 = 100 and the initial wages be W0 = 100 . - Initial Real Wage: RW0 = W0/P0 × 100 = 100/100 × 100 = 100 After the changes: - Price level increases by 10% P1 = 100 × 1.10 = 110 - Wages increase by 20% W1 = 100 × 1.20 = 120 - New Real Wage: RW1 = W1/P1 × 100 = 120/110 × 100 ≈ 109.09 The percentage increase in real wage is: Percentage Increase = RW1 - RW0 = 109.09 - 100 = 9.09% Since 9.09% is less than 10% , the real wage has increased by less than 10% . Hence, Option C is the correct answer.

If an increase of $10\%$ in prices. The rise in wages is $20\%$ then the real wage has increased by

The correct answer is Option c: Less than $10\%$. Let the initial price level be $P_0 = 100$ and the initial wages be $W_0 = 100$. - Initial Real Wage: $$RW_0 = \frac{W_0}{P_0} \times 100 = \frac{100}{100} \times 100 = 100$$ After the changes: - Price level increases by $10\%$ $\implies P_1 = 100 \times 1.10 = 110$ - Wages increase by $20\%$ $\implies W_1 = 100 \times 1.20 = 120$ - New Real Wage: $$RW_1 = \frac{W_1}{P_1} \times 100 = \frac{120}{110} \times 100 \approx 109.09$$ The percentage increase in real wage is: $$\text{Percentage Increase} = RW_1 - RW_0 = 109.09 - 100 = 9.09\%$$ Since $9.09\%$ is less than $10\%$, the real wage has increased by less than $10\%$. Hence, **Option C** is the correct answer.

Index NumbersMCQMTP Apr 21Question 3903 of 197

All Questions

If an increase of $\displaystyle 10\%$ in prices. The rise in wages is $\displaystyle 20\%$ then the real wage has increased by

Options

\displaystyle 20\%

\displaystyle 10\%

CLess than

\displaystyle 10\%

DMore than

\displaystyle 10\%

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Correct Answer

✅ Option c — Less than $\displaystyle 10\%$

All Options:

A $\displaystyle 20\%$
B $\displaystyle 10\%$
CLess than $\displaystyle 10\%$
DMore than $\displaystyle 10\%$

Detailed Solution & Explanation

Let the initial price level be

\displaystyle P_0 = 100

and the initial wages be

\displaystyle W_0 = 100

. - Initial Real Wage:

RW_0 = \frac{W_0}{P_0} \times 100 = \frac{100}{100} \times 100 = 100

After the changes: - Price level increases by

\displaystyle 10\%

\displaystyle \implies P_1 = 100 \times 1.10 = 110

- Wages increase by

\displaystyle 20\%

\displaystyle \implies W_1 = 100 \times 1.20 = 120

- New Real Wage:

RW_1 = \frac{W_1}{P_1} \times 100 = \frac{120}{110} \times 100 \approx 109.09

The percentage increase in real wage is:

\text{Percentage Increase} = RW_1 - RW_0 = 109.09 - 100 = 9.09\%

Since

\displaystyle 9.09\%

is less than

\displaystyle 10\%

, the real wage has increased by less than

\displaystyle 10\%

. Hence, **Option C** is the correct answer.

About This Chapter: Index Numbers

Paper

Paper 3: Quantitative Aptitude

Weightage

4-6 Marks

Key Topics

Construction of Index Numbers, Time Series

This chapter covers Construction of Index Numbers, Time Series and is part of Paper 3: Quantitative Aptitude in the CA Foundation exam.

View Official ICAI Syllabus

Exam Strategy Tip

This topic carries 4-6 Marks weightage. Focus on understanding core concepts rather than memorizing.

Related Comparison Tables

Cardinal vs Ordinal Utility: Measuring Satisfaction

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If an increase of 10%\displaystyle 10\%10% in prices. The rise in wages is 20%\displaystyle 20\%20% then the real wage has increased by