From the salary of a software engineer, if 15% is used as house rent, 25% of the remaining is spent on household items, 25% of the remaining as income tax, and 15% of the remaining on clothing, then he is left with Rs. 10,404. Find his total salary.

Given ;-

15% is used as house rent, 25% of the remaining is spent on household items, 25% of the remaining as income tax, and 15% of the remaining on clothing.

saving of engineer = Rs 10,404

Concept Use :-

Total salary = saving + expenditure

Calculation :-

Let Total salary of an engineer  's'

⇒ Expenditure on house rent = s × 0.15      [ use 15% = 15/100 = 0.15 ]

⇒ Remaining amount = s - s × 0.15 = s × 0.85

⇒ Expenditure on household items =  s × 0.85 × 0.25 = s × 0.2125

⇒ Remaining amount = s × 0.85 - s × 0.2125 =  s × 0.6375 

⇒  Expenditure on income tax = s × 0.6375 × 0.25 = s × 0.159375

⇒  Remaining amount =   s × 0.6375 -  s × 0.159375 = s × 0.478125

⇒ Expenditure on clothing = s × 0.478125 × 0.15 = s × 0.07171875

⇒  Remaining amount =  s × 0.478125 - s × 0.07171875 = s × 0.40640625

⇒  s × 0.40640625 = 10404 

⇒ s = 25,600

Alternate Method :-

⇒ s × (85/100) × (75/100) × (75/100) × (85/100) = 10,404 

⇒ s = (10404 × 100 × 100 × 100 × 100) / (85 × 75 × 75 × 85)

⇒ s = 25,600