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A man loses 20% of his money. After spending 25% of the remaining amount, he has ₹480 left. What is the amount of money he originally had?
₹800
₹600
₹720
₹840
₹800
Use successive percentage multipliers: remaining amount = original ×0.80×0.75=original×0.60. Therefore, 0.60×Original=480⟹Original=800.
A man loses 20% of his money. After spending 25% of the remaining amount, he has ₹480 left.
x×(1−10020)×(1−10025)=Remaining Amount
Use successive percentage multipliers: remaining amount = original ×0.80×0.75=original×0.60. Therefore, 0.60×Original=480⟹Original=800.
Students often add 20% and 25% to make 45% total reduction instead of calculating successive percentages.
Step 1: Understand the Losses and Remaindings
Let the original amount of money be x. After losing 20%, the remaining money is 80% of x, which is 0.80x.
0.80x
Step 2: Calculate Amount After Spending
He spends 25% of the remaining amount (0.80x). The amount left is (1−0.25)=75% of the remaining amount.
0.75×0.80x=0.60x
Step 3: Equate to Given Remaining Value
We are given that he has ₹480 left. Therefore, set 0.60x=480.
0.60x=480
Step 4: Solve for x
Solving for x, we get x=0.60480=₹800.
x=800
A is correct because the original amount of money is calculated as ₹800 after accounting for successive reductions of 20% and 25%.
Successive percentage changes are also heavily used in profit & loss, discount chains, and population growth problems.
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