Mr. More spent 20% of his monthly income on food and 15% on children's education. 40% of the remaining he spent on entertainment and transport together and 30% on medical. He is left with an amount of ₹ 8775 after all these expenditures. What is Mr. More's monthly income?

### Concept & Equation This problem uses grouped successive percentages. When expenses like "entertainment and transport" and "medical" are listed sequentially after "of the remaining," they share that new remaining amount as their common base. $$\text{Final Savings} = \text{Income} \times \left(1 - \frac{\sum R_{initial}}{100}\right) \times \left(1 - \frac{\sum R_{remaining}}{100}\right)$$ ### Step-by-Step Solution * Let Mr. More's total monthly income be $x$. * **First deduction phase:** He spends $20\%$ on food and $15\%$ on education. $$\text{First spend} = 20\% + 15\% = 35\%$$ $$\text{First remainder} = 100\% - 35\% = 65\% \text{ of } x$$ * **Second deduction phase:** Out of this $65\%$, he spends $40\%$ on entertainment/transport and $30\%$ on medical. $$\text{Second spend} = 40\% + 30\% = 70\% \text{ of the remainder}$$ * **Final savings:** If he spends $70\%$ of the remainder, he saves $30\%$ of the remainder. $$\text{Savings} = 30\% \text{ of } 65\% \text{ of } x = 8775$$ $$0.30 \times 0.65 \times x = 8775$$ $$0.195x = 8775$$ * **Calculate Total Income:** $$x = \frac{8775}{0.195} = \frac{8775000}{195}$$ $$x = 45000$$ ### Exam Strategy & Shortcut Use fractional multipliers based on what is *left over* at each phase. Phase 1: Spends $35\%$, keeps $65\%$ (which is $\frac{13}{20}$). Phase 2: Spends $70\%$ of the remainder, keeps $30\%$ (which is $\frac{3}{10}$). $$x \times \frac{13}{20} \times \frac{3}{10} = 8775$$ $$x \times \frac{39}{200} = 8775$$ $$x = \frac{8775 \times 200}{39} = 225 \times 200 = 45000$$ Since ₹ 45000 is not in the options (a, b, c, d), the answer is (e). ### Common Pitfall Misinterpreting "and 30% on medical" as being $30\%$ of the *total* initial income rather than continuing the established "of the remaining" base. Grouping logic is critical in banking exam phrasing. ### Final Answer **Therefore, the correct answer is None of these.**