Question:

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
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The Correct Option is C

Solution and Explanation

Step 1: Read the two percentages carefully.
The 20% for rent is taken on the total income.
The 70% for household expenditure is taken on the remaining amount, not on the total income. Missing this shift of base is the main trap in the question.
Let the total income be \( I \) rupees.

Step 2: Work out the rent and what is left after it.
Rent \( = 20\% \text{ of } I = 0.2I \).
Remaining \( = I - 0.2I = 0.8I \).

Step 3: Work out the household expenditure.
Household \( = 70\% \text{ of } 0.8I = 0.7 \times 0.8I = 0.56I \).
Note this is 56% of the total income, not 70% of it.

Step 4: Find the savings as a fraction of income.
What is left over is the saving:
\[ \text{Savings} = 0.8I - 0.56I = 0.24I \]
Another way to see it: after rent, 70% is spent, so 30% of the remaining amount is saved, and \( 0.3 \times 0.8I = 0.24I \). Both views agree.

Step 5: Solve for the income.
\[ 0.24I = 1800 \]
\[ I = \frac{1800}{0.24} = \frac{180000}{24} = 7500 \]

Step 6: Verify the whole budget.
Rent \( = 0.2 \times 7500 = 1500 \).
Remaining \( = 7500 - 1500 = 6000 \).
Household \( = 0.7 \times 6000 = 4200 \).
Savings \( = 6000 - 4200 = 1800 \). This matches the question exactly.

Step 7: Why the other options are wrong.
Rs. 8000 gives savings of \( 0.24 \times 8000 = 1920 \), too much.
Rs. 9500 gives \( 0.24 \times 9500 = 2280 \).
Rs. 8500 gives \( 0.24 \times 8500 = 2040 \).
Only Rs. 7500 lands on exactly Rs. 1800. If someone wrongly took 70% of the total income, savings would be 10% of income and the answer would come out as Rs. 18000, which is not even listed.

Final Answer:
The total income is Rs. 7500. \[ \boxed{\text{Rs. } 7500} \]
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