Shortcut Trick
Income Ratio (A:V) = 3:2 (Diff = 1); Expense Ratio (A:V) = 7:3 (Diff = 4)
Make differences equal: Multiply Income Ratio by 4 → 12:8
Saving (equal for both) = Income − Expense = 12 − 7 = 5 units
5 units = ₹1,80,000 ⇒ 1 unit = ₹36,000
Akshay's Annual Income = 12 units = 12 × ₹36,000 = ₹4,32,000
∴ The correct answer is ₹4,32,000.
Alternate Method
Given:
Ratio of Annual Income (Akshay : Vipul) = 3 : 2
Ratio of Expenses (Akshay : Vipul) = 7 : 3
Savings for each = ₹1,80,000
Let Akshay's income be 3x and Vipul's income be 2x.
Since Income − Savings = Expense:
⇒ (3x − 1,80,000) ÷ (2x − 1,80,000) = 7 ÷ 3
⇒ 3 × (3x − 1,80,000) = 7 × (2x − 1,80,000)
⇒ 9x − 5,40,000 = 14x − 12,60,000
⇒ 14x − 9x = 12,60,000 − 5,40,000
⇒ 5x = 7,20,000
⇒ x = 1,44,000
⇒ Akshay's Annual Income = 3x = 3 × 1,44,000
⇒ Akshay's Annual Income = ₹4,32,000
∴ The correct answer is ₹4,32,000.
Additional Information
Income-Expense Relationship
The fundamental relation is Income = Expenditure + Savings. If savings are equal, the difference between income units and expenditure units must be made equal.
Cross-Multiplication Method
For two ratios a:b and c:d with a constant addition/subtraction k, use |ad − bc| units = k × |c − d| to find the value of one unit.
Ratio Balancing
When the change in both terms of a ratio is the same, multiply each ratio by the difference of the other ratio to equalize the numeric difference between corresponding terms.