The income of S, T and U are in the ratio of 7 : 9 : 6 and their expenses in the ratio of 4 : 5 : 3. If S saves Rs 2000 out of an income of Rs. 14000, then what will be the saving (in Rs) of T?

Options

A. 2400
B. 1500
C. 3000
D. 2000

Answer

To solve the problem step by step, we will follow the given ratios and the information provided about S's income and savings.

### Step 1: Determine the Income of T
We know the income ratios of S, T, and U are 7:9:6. Given that S's income is Rs 14,000, we can set up the following proportion to find T's income.

Let the common multiplier be \( x \).
- Income of S = \( 7x \)
- Income of T = \( 9x \)
- Income of U = \( 6x \)

Since S's income is Rs 14,000:
\[ 7x = 14000 \implies x = \frac{14000}{7} = 2000 \]

Now, we can find T's income:
\[ \text{Income of T} = 9x = 9 \times 2000 = 18000 \]

### Step 2: Calculate S's Expenditure
We know S saves Rs 2000 from his income of Rs 14,000. Therefore, S's expenditure can be calculated as:
\[ \text{Expenditure of S} = \text{Income of S} - \text{Savings of S} = 14000 - 2000 = 12000 \]

### Step 3: Determine the Expenditure Ratios
The expenditure ratios of S, T, and U are given as 4:5:3. We can set up a similar proportion for their expenditures.

Let the common multiplier for expenditures be \( y \).
- Expenditure of S = \( 4y \)
- Expenditure of T = \( 5y \)
- Expenditure of U = \( 3y \)

From Step 2, we know S's expenditure is Rs 12,000:
\[ 4y = 12000 \implies y = \frac{12000}{4} = 3000 \]

### Step 4: Calculate T's Expenditure
Now we can find T's expenditure:
\[ \text{Expenditure of T} = 5y = 5 \times 3000 = 15000 \]

### Step 5: Calculate T's Savings
Finally, we can calculate T's savings:
\[ \text{Savings of T} = \text{Income of T} - \text{Expenditure of T} = 18000 - 15000 = 3000 \]

### Conclusion
Thus, the savings of T is Rs 3000.

---