Shortcut Trick
Apply Cross-Product Method for Ratio problems with constant change:
Income Ratio = 6 : 8 | Expenditure Ratio = 2 : 3 | Savings = ₹33,000 each
Difference in units = (6 × 3 − 8 × 2) = 18 − 16 = 2 units
Difference in value = 33,000 × (3 − 2) = ₹33,000
2 units = ₹33,000 ⇒ 1 unit = ₹16,500
Shivam's Income = 6 units = 6 × 16,500 = ₹99,000
∴ The correct answer is ₹99,000.
Alternate Method
Given:
Ratio of Income (Shivam : Rupesh) = 6 : 8
Ratio of Expenditure (Shivam : Rupesh) = 2 : 3
Savings of each = ₹33,000
Formula Used: Income − Savings = Expenditure
To equalize the difference between Income and Expenditure units:
⇒ Diff in Income parts = 8 − 6 = 2
⇒ Diff in Expenditure parts = 3 − 2 = 1
⇒ Multiply Expenditure Ratio by 2 ⇒ (2 : 3) × 2 = 4 : 6
⇒ Now, Shivam's Income : Expenditure = 6 : 4
⇒ Savings = 6 − 4 = 2 units
⇒ 2 units = ₹33,000
⇒ 1 unit = 33,000 ÷ 2 = ₹16,500
⇒ Shivam's monthly income = 6 × 16,500 = ₹99,000
∴ The correct answer is ₹99,000.
Additional Information
Income-Expenditure Relation
Basic formula: Income = Expenditure + Savings. All calculations must use the same unit/base.
Ratio Balancing Method
When the absolute value of change (savings) is the same for both entities, multiply the terms of one ratio by the difference of the other to make unit gaps equal.
Cross-Multiplication Formula
For ratios a:b and c:d with common saving S, value of 1 unit = [S × (d − c)] ÷ (ad − bc).