Shortcut Trick
The Income Ratio of Ramesh and Suresh is 3 : 4 and their Expenditure Ratio is 2 : 3.
Since the difference between income and expenditure units is the same (3 − 2 = 1 and 4 − 3 = 1), 1 unit represents the Savings.
Given Savings = ₹200 ⇒ 1 unit = ₹200.
Ramesh's Income = 3 units = 3 × 200 = ₹600.
Suresh's Income = 4 units = 4 × 200 = ₹800.
∴ The correct answer is ₹600 and ₹800.
Alternate Method
Given:
Ratio of Income = 3 : 4
Ratio of Expenditure = 2 : 3
Savings of each = ₹200
Formula Used:
Income − Expenditure = Savings
Calculations:
Let the Income of Ramesh and Suresh be 3x and 4x respectively.
Let the Expenditure of Ramesh and Suresh be 2y and 3y respectively.
According to the question:
⇒ 3x − 2y = 200 ... (Equation 1)
⇒ 4x − 3y = 200 ... (Equation 2)
From (1) and (2), we have:
⇒ 3x − 2y = 4x − 3y
⇒ 3y − 2y = 4x − 3x
⇒ y = x
Substituting y = x in Equation 1:
⇒ 3x − 2x = 200
⇒ x = 200
Now, finding the Incomes:
⇒ Ramesh's Income = 3x = 3 × 200 = ₹600
⇒ Suresh's Income = 4x = 4 × 200 = ₹800
∴ The correct answer is ₹600 and ₹800.
Additional Information
Income-Expenditure-Savings Relation
The basic relationship is always Income = Expenditure + Savings. For two people, if savings are equal, the differences between their income and expenditure ratios must be made equal.
Ratio Balancing Method
If the difference between Income parts and Expenditure parts is not equal, multiply the ratios by the difference of the other ratio to balance them (e.g., multiply the first ratio by the difference of the second ratio).
Percentage Conversion
Income and expenditure problems can also be solved using Percentages where Income is considered as 100% and Savings % = 100% − Expenditure %.