Correct Answer - Option 3 : Rs. 27000
Given:
Ram’s income is 25% more than his wife
Ram’s savings is 10% less than his wife.
Total savings of Ram and his wife is Rs. 28500
Ram’s expenditure is 3/5th of salary
Concept:
Income is equal to sum of savings and expenditure
Formula:
Savings = (1 – x) part of salary
When, x part of salary is the expenditure
R = (100 + x)% of V
When R is x% more than V
V = R × 100/(100 + x)
When R is x% more than V
V = R × 100/(100 – x)
When R is x% less than V
Calculation:
Let Ram’s wife’s income be x
Ram’s salary = 125% of x = 5/4x
Rams savings = (1 – 3/5) × 5/4x
⇒ Ram’s savings = 2/5 × 5/4x
⇒ Ram’s savings = 1/2x
Ram’s wife’s savings = 1/2x × 100/90 = 5/9x
Total savings of Ram and his wife = 1/2x + 5/9x = 19/18x
19/18x = 28500
⇒ x = (28500 × 18)/19
⇒ x = 1500 × 18
⇒ x = 27000
∴ Ram’s wife’s income is Rs. 27000