Ratio Problem: Calculating A's Savings

This problem involves calculating savings based on given income and expense ratios.

Given Information

• Income Ratio (A : B) = 5 : 3
• Expense Ratio (A : B : C) = 8 : 5 : 2
• C's Expense = ₹2000
• B's Savings = ₹700

Step 1: Calculate Actual Expenses

We know C's expense and the expense ratio (A : B : C = 8 : 5 : 2). Let the common multiplier for expenses be '$x$'.

• C's Expense = $2x$
• $2x = ₹2000$
• $x = \frac{₹2000}{2} = ₹1000$

Now, we can find the expenses of A and B:

• A's Expense = $8x = 8 \times ₹1000 = ₹8000$
• B's Expense = $5x = 5 \times ₹1000 = ₹5000$

Step 2: Calculate B's Income

Savings = Income - Expense. We know B's Expense and B's Savings.

• B's Income = B's Expense + B's Savings
• B's Income = $₹5000 + ₹700 = ₹5700$

Step 3: Calculate A's Income

We know B's income and the income ratio (A : B = 5 : 3). Let the common multiplier for income be '$y$'.

• B's Income = $3y$
• $3y = ₹5700$
• $y = \frac{₹5700}{3} = ₹1900$

Now, calculate A's income:

• A's Income = $5y = 5 \times ₹1900 = ₹9500$

Step 4: Calculate A's Savings

A's Savings = A's Income - A's Expense

• A's Savings = $₹9500 - ₹8000 = ₹1500$

Therefore, A saves ₹1500.