Subjects algebra

Money Spent D4D0Df

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1. **Problem statement:** A man spends 12.5% of his money. After spending 75% of the remainder, he has 175 left. We need to find the original amount of money he had. 2. **Define variables:** Let the original amount be $x$. 3. **Step 1: Calculate money left after spending 12.5%.** He spends 12.5% of $x$, so he spends $\frac{12.5}{100}x = 0.125x$. Money left after this spending is: $$x - 0.125x = 0.875x$$ 4. **Step 2: Calculate money left after spending 75% of the remainder.** He spends 75% of the remainder $0.875x$, which is: $$\frac{75}{100} \times 0.875x = 0.75 \times 0.875x = 0.65625x$$ Money left after this second spending is: $$0.875x - 0.65625x = 0.21875x$$ 5. **Step 3: Set the money left equal to 175 and solve for $x$.** $$0.21875x = 175$$ Divide both sides by 0.21875: $$x = \frac{175}{0.21875}$$ 6. **Step 4: Simplify the division.** Note that $0.21875 = \frac{7}{32}$, so: $$x = \frac{175}{\frac{7}{32}} = 175 \times \frac{32}{7}$$ Simplify $\frac{175}{7} = 25$: $$x = 25 \times 32 = 800$$ 7. **Answer:** The man originally had Rs 800. **Final answer:** Rs 800