Question:easy

Out of the total income, X spends 20% on house rent and 70% of the remaining amount on household expenditure. If X saves Rs. 1800, the total income is

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The 70% applies to what is left after rent, not to the whole income. Savings = 30% of 80% of income = 24% of income, and 24% of the income is 1800.
Updated On: Jul 17, 2026
  • Rs. 8000
  • Rs. 9500
  • Rs. 7500
  • Rs. 8500
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Pick a convenient trial income.
Percentages scale, so start with an income of Rs. 100 and see what the saving works out to.

Step 2: Run the budget on Rs. 100.
Rent is $20\%$ of 100, which is Rs. 20.
What is left is $100 - 20 = 80$.
Household spending is $70\%$ of that Rs. 80, which is $\dfrac{70}{100} \times 80 = 56$.
Saving is $80 - 56 = 24$.
So on every Rs. 100 of income, exactly Rs. 24 is saved.

Step 3: Scale up to the real saving.
Savings of Rs. 24 correspond to an income of Rs. 100.
Savings of Rs. 1800 correspond to
\[ \frac{100}{24} \times 1800 = 100 \times 75 = 7500 \]

Step 4: A fraction based view.
After rent the man keeps $\dfrac{4}{5}$ of his income. Of that he saves $\dfrac{3}{10}$, since $70\%$ goes on the household.
\[ \text{Saving fraction} = \frac{4}{5} \times \frac{3}{10} = \frac{12}{50} = \frac{6}{25} \]
\[ \frac{6}{25} I = 1800 \quad \Rightarrow \quad I = 1800 \times \frac{25}{6} = 300 \times 25 = 7500 \]

Step 5: Check the options against the 24% rule.
Since the saving is always $24\%$ of income, the income must be a number whose $24\%$ is 1800.
Rs. 8000 saves 1920, Rs. 8500 saves 2040, Rs. 9500 saves 2280. All overshoot.
Rs. 7500 saves $0.24 \times 7500 = 1800$, an exact hit.

Final Answer:
X earns Rs. 7500 in total. \[ \boxed{\text{Rs. } 7500} \]
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