The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
₹1500
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.
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