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A person gave 40% of his income to his wife to look after household expenditure. He gave 20% of the remaining amount to each of his two sons and one daughter. One - third of the amount now left was spent on miscellaneous items and the remaining amount ₹14,400 was deposited in the bank. Find his income.
₹90,000
₹96,000
₹1,10,000
₹1,00,000
₹90,000
Work backward from ₹14,400. Since 1/3 was spent on miscellaneous, 2/3 remains, so the amount before misc was 14,400×3/2=21,600. Then work through the percentages.
Initial income share to wife: 40%. Remaining share given to 3 children: 20% each. Remaining amount balance after misc expense: ₹14,400.
X×(1−r1)×(1−r2)×(1−r3)=Remaining Amount
Work backward from ₹14,400. Since 1/3 was spent on miscellaneous, 2/3 remains, so the amount before misc was 14,400×3/2=21,600. Then work through the percentages.
Students often add the percentages (40% + 20% + 20% + 20%) instead of applying them sequentially on the remaining balance.
Calculate remaining balance after family expenses
After giving 40% to his wife, 60% remains. From this, he gives 20% to each of 3 children (60% total of the remainder). Thus, 40% of the remainder is left: 0.60×(1−0.60)=0.60×0.40=0.24 of total income.
0.60×0.40=0.24
Account for miscellaneous expenditure
One-third was spent on miscellaneous items, meaning two-thirds of the current balance remains: 0.24×32=0.16 of total income.
0.24×32=0.16
Solve for total income
The final amount is 16% of the income, which equals ₹14,400: 0.16×X=14,400. Therefore, X=0.1614400=90,000.
X=0.1614400=90,000
A is correct because calculating the sequence of deductions reveals that 16% of the total income is ₹14,400, resulting in an income of ₹90,000.
This 'Successive Percentage' model is identical to 'Successive Discount' or 'Population Growth' problems where you multiply by the growth/decay factor at each step.
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