The income of X, Y and Z are in the ratio of 3 : 4 : 2 and their expenses in the ratio of 5 : 5 : 2. If X saves Rs 3000 out of an income of Rs 18000, then what will be the saving (in Rs) of Y?

Options

A. 4500
B. 9000
C. 6000
D. 7500

Explanation

To solve the problem step by step, we will follow the given ratios for income and expenses, and use the information provided about X's savings to find Y's savings.

### Step 1: Understand the Ratios
The incomes of X, Y, and Z are in the ratio of 3:4:2. Let’s denote their incomes as:
- Income of X = 3a
- Income of Y = 4a
- Income of Z = 2a

The expenses of X, Y, and Z are in the ratio of 5:5:2. Let’s denote their expenses as:
- Expense of X = 5b
- Expense of Y = 5b
- Expense of Z = 2b

### Step 2: Find the Value of 'a'
We know that X's income is Rs 18,000. Therefore, we can set up the equation:
\[ 3a = 18000 \]
To find 'a', we divide both sides by 3:
\[ a = \frac{18000}{3} = 6000 \]

### Step 3: Calculate the Incomes of Y and Z
Now that we have the value of 'a', we can find the incomes of Y and Z:
- Income of Y = 4a = 4 × 6000 = Rs 24000
- Income of Z = 2a = 2 × 6000 = Rs 12000

### Step 4: Find X's Expenses
We know that X saves Rs 3000 from his income of Rs 18000. Therefore, we can calculate X's expenses:
\[ \text{Expenses of X} = \text{Income of X} - \text{Savings of X} \]
\[ \text{Expenses of X} = 18000 - 3000 = Rs 15000 \]

### Step 5: Find the Value of 'b'
From the expense ratio, we have:
\[ 5b = 15000 \]
To find 'b', we divide both sides by 5:
\[ b = \frac{15000}{5} = 3000 \]

### Step 6: Calculate Y's Expenses
Now, we can find Y's expenses using the value of 'b':
\[ \text{Expenses of Y} = 5b = 5 × 3000 = Rs 15000 \]

### Step 7: Calculate Y's Savings
Finally, we can calculate Y's savings:
\[ \text{Savings of Y} = \text{Income of Y} - \text{Expenses of Y} \]
\[ \text{Savings of Y} = 24000 - 15000 = Rs 9000 \]

### Final Answer
The savings of Y will be Rs 9000.

---