The ratio of expenditures of Lakshmi and Meenakshi is $2 : 3$, and the ratio of income of Lakshmi to expenditure of Meenakshi is $6 : 7$. If excess of income over expenditure is saved by Lakshmi and Meenakshi, and the ratio of their savings is $4 : 9$, then the ratio of their incomes is:
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- \(7 : 8\)
- \(3 : 5\)
- \(2 : 1\)
- \(5 : 6\)
The Correct Option is B
Approach Solution - 1
Step 1: Assume the expenditures. Let the expenditure of Lakshmi be \[ E_L = 2x \] and that of Meenakshi be \[ E_M = 3x. \] Step 2: Use the given ratio of Lakshmi’s income to Meenakshi’s expenditure. It is given that \[ \frac{I_L}{E_M} = \frac{6}{7}. \] Substituting \(E_M = 3x\), \[ \frac{I_L}{3x} = \frac{6}{7} \Rightarrow I_L = \frac{18x}{7}. \] Step 3: Express the savings. Savings are equal to income minus expenditure. Lakshmi’s savings are \[ S_L = I_L - E_L = \frac{18x}{7} - 2x = \frac{18x - 14x}{7} = \frac{4x}{7}. \] Let Meenakshi’s income be \(I_M\). Then her savings are \[ S_M = I_M - 3x. \] Step 4: Apply the ratio of savings. Given that \[ S_L : S_M = 4 : 9, \] we have \[ \frac{\frac{4x}{7}}{I_M - 3x} = \frac{4}{9}. \] Cancelling 4 from both sides, \[ \frac{\frac{x}{7}}{I_M - 3x} = \frac{1}{9}. \] Thus, \[ 9 \cdot \frac{x}{7} = I_M - 3x \Rightarrow I_M = \frac{9x}{7} + 3x = \frac{9x + 21x}{7} = \frac{30x}{7}. \] Step 5: Find the ratio of incomes. \[ \frac{I_L}{I_M} = \frac{\frac{18x}{7}}{\frac{30x}{7}} = \frac{18}{30} = \frac{3}{5}. \] Hence, the ratio of Lakshmi’s income to Meenakshi’s income is \[ 3 : 5. \]
Approach Solution -2
Step 2: Use the ratio of income of Lakshmi to expenditure of Meenakshi: \[ \frac{I_L}{E_M} = \frac{6}{7} \;\Rightarrow\; \frac{I_L}{3x} = \frac{6}{7} \;\Rightarrow\; I_L = \frac{18x}{7}. \]
Step 3: Find savings. Savings = Income $-$ Expenditure. Lakshmi’s savings: \[ S_L = I_L - E_L = \frac{18x}{7} - 2x = \frac{18x - 14x}{7} = \frac{4x}{7}. \] Let $I_M$ be Meenakshi’s income. Then her savings: \[ S_M = I_M - E_M = I_M - 3x. \]
Step 4: Use the savings ratio $S_L : S_M = 4 : 9$: \[ \frac{S_L}{S_M} = \frac{4}{9} \;\Rightarrow\; \frac{\frac{4x}{7}}{I_M - 3x} = \frac{4}{9}. \] Divide both sides by $4$: \[ \frac{\frac{x}{7}}{I_M - 3x} = \frac{1}{9} \;\Rightarrow\; 9\cdot\frac{x}{7} = I_M - 3x \;\Rightarrow\; I_M = \frac{9x}{7} + 3x = \frac{9x + 21x}{7} = \frac{30x}{7}. \]
Step 5: Ratio of incomes: \[ \frac{I_L}{I_M} = \frac{\frac{18x}{7}}{\frac{30x}{7}} = \frac{18}{30} = \frac{3}{5}. \] Therefore, the ratio of Lakshmi’s income to Meenakshi’s income is \(3 : 5\).
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In the dynamic realm of creativity, artists often find themselves at the crossroads between drawing inspiration from diverse cultures and inadvertently crossing into the territory of cultural appropriation. Inspiration is the lifeblood of creativity, driving artists to create works that resonate across borders. In a globalized era of the modern world, artists draw from a vast array of cultural influences. When approached respectfully, inspiration becomes a bridge, fostering understanding and appreciation of cultural diversity. However, the line between inspiration and cultural appropriation can be thin and easily blurred.
Cultural appropriation occurs when elements from a particular culture are borrowed without proper understanding, respect, or acknowledgment. This leads to the commodification of sacred symbols, the reinforcement of stereotypes, and the erasure of the cultural context from which these elements originated. It is essential to recognize that the impact of cultural appropriation extends beyond the realm of artistic expression, influencing societal perceptions and perpetuating power imbalances.- CAT - 2025
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