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Mr. Amit spends 40% of his income on house rent and 20% of the remaining amount on education. He saves half of the remaining amount every month. If he saves 12,000 every month, then find his monthly income.
40000
50000
60000
75000
50000
Given: Rent expenditure is 40% of income. Education expenditure is 20% of the remaining amount. Savings is 50% of the final remainder, which equals 12,000.
Rent expenditure is 40% of income. Education expenditure is 20% of the remaining amount. Savings is 50% of the final remainder, which equals 12,000.
I=Remaining┬аFraction┬аProduct├ЧSavings┬аFractionSтАЛ
Use the fraction product method: Income = Savings / [(1 - 0.4) * (1 - 0.2) * 0.5]. Calculate the net fraction of the remaining balance: 0.6 * 0.8 * 0.5 = 0.24. Then, 12,000 / 0.24 = 50,000.
Students often add percentages (40% + 20% = 60%) and calculate savings on the original income instead of the successive remaining balances.
Calculate the successive remaining fractions
After spending 40% on rent, 60% (or 0.6) remains. After spending 20% of that remainder on education, 80% of the remainder is left: 0.6├Ч0.8=0.48.
0.6├Ч0.8=0.48
Incorporate the savings fraction
Mr. Amit saves 50% of the remaining 48% of his income. Thus, his total savings is 50% of 0.48 of his total income I.
Savings=0.48├Ч0.50├ЧI=0.24I
Solve for total income
Set the calculated savings equal to the given amount of 12,000 and solve for I.
0.24I=12000тЯ╣I=0.2412000тАЛ=50000
B is correct because the successive calculation of the remaining income leads to 24% of the original income equaling 12,000, resulting in an income of 50,000.
This concept of successive reduction is identical to calculating compound interest or population growth/decay models in different contexts.