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Out of his total income, Sanjay spends 20% on house rent and 70% of the rest on household expenses. If he saves ₹1,800, then his total income is:
₹10,000
₹7,500
₹8,000
₹9,000
₹7,500
Use successive percentage reductions: 20% rent leaves 80%, and 70% of the rest leaves 30% of that 80%. So savings = 0.80×0.30×Income=0.24×Income.
Sanjay spends 20% of his total income on house rent, 70% of the remaining amount on household expenses, and saves ₹1,800.
Income×(1−10020)×(1−10070)=Savings
Use successive percentage reductions: 20% rent leaves 80%, and 70% of the rest leaves 30% of that 80%. So savings = 0.80×0.30×Income=0.24×Income.
Taking 70% of the total income instead of 70% of the remaining amount after paying house rent.
Step 1: Define variables and calculate remaining amount after house rent
Let Sanjay's total income be I. He spends 20% of his income on house rent. The remaining amount is 80% of his income.
Remaining=I×(1−10020)=0.80I
Step 2: Calculate savings after household expenses
He spends 70% of the remaining amount on household expenses, which means he saves the other 30% of the remaining amount.
Savings=0.80I×(1−10070)=0.80I×0.30=0.24I
Step 3: Equate savings to given amount and solve for total income
Given that his savings equal ₹1,800, we equate 0.24I to 1800 to find I.
0.24I=1800⟹I=0.241800=7500
B is correct because calculating 30% of the remaining 80% of his income gives 0.24I=1800, which yields a total income of ₹7,500.
Successive percentage problems frequently appear in profit-loss and population growth chapters; always calculate the remaining multiplier sequentially.
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