The incomes of X, Y and Z are in the ratio 3 : 4 : 2 and their expenses are in the ratio 5 : 5 : 2. If X saves Rs. 3000 out of an income of Rs. 18,000, then what will be the saving of Y in rupees?

Introduction / Context:
This problem connects ratios of income and expenditure with the concept of savings. Such questions are popular in aptitude and banking exams because they test the ability to move between income, expense, and saving using proportional relationships. Here, incomes and expenses of three persons X, Y, and Z are given in two different ratios, and we are asked to find the saving of Y using the given saving of X as a reference point.

Given Data / Assumptions:

• Income ratio of X : Y : Z is 3 : 4 : 2.
• Expense ratio of X : Y : Z is 5 : 5 : 2.
• Income of X is Rs. 18,000.
• Saving of X is Rs. 3000.
• Savings = Income - Expenses for each person.

Concept / Approach:
The plan is to use X as the reference. First, we know X’s actual income and saving, so we can compute X’s actual expenditure. From X’s expenditure and given expense ratio, we can find the common multiplier for expenses. That allows us to calculate Y’s actual expenditure. Then, using the income ratio and X’s actual income, we find Y’s income. Finally, we compute Y’s saving as income minus expenditure. This stepwise use of ratios is the core idea behind the solution.

Step-by-Step Solution:

Verification / Alternative check:
We can also compute Z to verify consistency. Z’s expense = 2m = 2 * 3,000 = 6,000. Z’s income = 2k = 2 * 6,000 = 12,000. Z’s saving = 12,000 - 6,000 = 6,000. All values are positive and align with the given ratios, so the model is coherent and the saving of Y as 9,000 is reliable.

Why Other Options Are Wrong:

• 4500: This would require either income or expenses of Y to violate the given ratios.
• 6000: This would make Y’s saving equal to Z’s saving, which does not follow from the computed incomes.
• 7500: This value does not correspond to the precise ratio-based calculations of income and expenses.

Common Pitfalls:
Students often confuse the income ratio with the expense ratio or attempt to directly apply ratios to savings. Another mistake is to wrongly assume that savings are in a simple ratio, which is usually not true. The correct method is always: use ratios to find absolute income and expense, then compute savings as the difference. Carefully maintaining two separate ratios is crucial.

Final Answer:
The saving of Y is Rs. 9,000.