Asha's monthly income is $60\%$ of Deepak's monthly income and $120\%$ of Maya's monthly income. What is Maya's monthly income if Deepak's monthly income is ₹ 78000?

### Concept & Logic This problem tests chained percentage relationships. Instead of finding complex ratios between all three individuals simultaneously, calculate the linking variable (Asha's income) first using the concrete value provided (Deepak's income), and then work backward to find Maya's income. ### Step-by-Step Solution * **Given:** Asha's Income ($A$) = $60\%$ of Deepak's Income ($D$). Asha's Income ($A$) = $120\%$ of Maya's Income ($M$). Deepak's Income ($D$) = ₹ $78000$. * **Calculation / Deduction:** First, calculate Asha's actual income using Deepak's value: $$A = \frac{60}{100} \times 78000$$ $$A = 60 \times 780 = 46800$$ So, Asha earns ₹ $46800$. Next, use Asha's income to find Maya's income: We know $A = 1.20 \times M$. Substitute the value of $A$: $$46800 = 1.20 \times M$$ $$M = \frac{46800}{1.20}$$ $$M = \frac{468000}{12}$$ $$M = 39000$$ ### Exam Strategy & Shortcut Use fractions instead of percentages for quicker mental math. $60\% = \frac{3}{5}$ and $120\% = \frac{6}{5}$. $A = \frac{3}{5} \times 78000$. You don't even need to fully solve this right away. We know $A = \frac{6}{5} \times M$. Therefore, $\frac{6}{5} \times M = \frac{3}{5} \times 78000$. Cancel out the denominators ($5$): $6 \times M = 3 \times 78000$ $M = \frac{1}{2} \times 78000 = 39000$. This fractional equivalence method completely skips the intermediate step of finding Asha's exact income and saves significant time! ### Common Pitfall A very common mistake is calculating Maya's income as $120\%$ of Deepak's or getting the inverse relationship wrong (i.e., calculating Maya as $120\%$ of Asha rather than Asha being $120\%$ of Maya). Always write down the linear equation exactly as the sentence reads before plugging in numbers. ### Final Answer **Therefore, the correct answer is ₹ 39000.**