Ratio and Proportion: The ratio of the monthly incomes of A, B, and C is 2:3:4 and their monthly expenses are in the ratio 5:6:7. If A saves Rs. 1,000, B saves Rs. 2,000, find C’s savings.

Step 1: Let monthly incomes be

A = 2x

B = 3x

C = 4x

Let monthly expenses be:

A = 5y

B = 6y

C = 7y

Step 2: Use savings info

A’s savings = 2x – 5y = 1000

B’s savings = 3x – 6y = 2000

Step 3: Solve the system

From A: 2x – 5y = 1000 From B: 3x – 6y = 2000

Multiply A’s equation by 3: → 6x – 15y = 3000 Multiply B’s equation by 2: → 6x – 12y = 4000

Now subtract: (6x – 15y) – (6x – 12y) = 3000 – 4000 → –3y = –1000 → y = 333.33 Plug into A’s equation: 2x – 5(333.33) = 1000 → 2x – 1666.67 = 1000 → 2x = 2666.67 → x = 1333.33

Step 4: Find C’s savings

Income = 4x = 4 × 1333.33 = 5333.33 Expense = 7y = 7 × 333.33 = 2333.33 Savings = 5333.33 – 2333.33 = ₹3000