Shortcut Trick
Apply the cross-multiplication method for ratio problems with constant change.
Salary Ratio (A : B) = 3 : 5 | Expenditure Ratio (A : B) = 4 : 7 | Savings = Rs. 7000 each.
Cross-product of ratios: (3 × 7) − (5 × 4) = 21 − 20 = 1 unit.
Cross-product with values: 7000 × (7 − 4) = 7000 × 3 = 21000.
Equating: 1 unit = Rs. 21000 ⇒ B's Salary = 5 units = 5 × 21000 = Rs. 105000.
∴ The correct answer is Rs. 105000.
Alternate Method
Given: Monthly salary ratio of A and B = 3 : 5, Expenditure ratio = 4 : 7, Savings of each = Rs. 7000.
Formula Used: Income − Expenditure = Savings
⇒ Let the monthly salary of A and B be 3x and 5x respectively.
⇒ Let their monthly expenditures be 4y and 7y respectively.
⇒ 3x − 4y = 7000 → (Equation 1)
⇒ 5x − 7y = 7000 → (Equation 2)
⇒ From Eq 1 and Eq 2: 3x − 4y = 5x − 7y
⇒ 7y − 4y = 5x − 3x
⇒ 3y = 2x ⇒ y = 2x/3
⇒ Substitute y in Eq 1: 3x − 4(2x/3) = 7000
⇒ (9x − 8x)/3 = 7000
⇒ x/3 = 7000 ⇒ x = 21000
⇒ Salary of B = 5x = 5 × 21000 = Rs. 105000.
∴ The correct answer is Rs. 105000.
Additional Information
Income, Expenditure and Savings Relationship
The fundamental relation is Income = Expenditure + Savings. When savings are equal for two individuals, the difference in their income units must be adjusted to match the difference in their expenditure units.
Ratio Balancing Method
If the difference between income units (5−3=2) and expenditure units (7−4=3) is not the same, we multiply the ratios by the difference of the other ratio to balance the units representing the savings.
Percentage of Savings
Savings % = (Savings ÷ Total Income) × 100. This is useful for comparing financial health across different income brackets.