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Out of his total income, Ravi spends 30% on groceries and 50% of the rest on travel. If he saves 2,100, then his total income is:
5000
6000
7000
8000
6000
Use the multiplier method: 2100÷(0.7×0.5)=2100÷0.35=6000. Or simply notice 0.7×0.5=0.35 represents the savings fraction.
Expenditure on groceries = 30%, expenditure on travel = 50% of the remaining amount, final savings = 2,100.
Total Income=(1−p1)(1−p2)Savings
Use the multiplier method: 2100÷(0.7×0.5)=2100÷0.35=6000. Or simply notice 0.7×0.5=0.35 represents the savings fraction.
Students often add the percentages (30% + 50% = 80%) and subtract from 100% to assume 20% savings, ignoring that 50% is calculated on the 'rest' (remaining 70%).
Calculate remaining income after groceries
If Ravi spends 30% of his income, he is left with 70% of his total income.
100%−30%=70%=0.7
Calculate remaining income after travel
Ravi spends 50% of the 'rest' on travel, which means he is left with another 50% of that remaining 70%.
0.7×0.5=0.35
Determine total income
Since 35% of the total income is equal to 2,100, divide the savings by the fraction to find the total.
Total Income=0.352100=6000
B is correct because calculating the successive remainders reveals that 35% of the total income equals 2,100, resulting in 6,000.
This concept of 'successive reduction' is identical to calculating compound depreciation or successive discounts in Profit and Loss chapters.
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