Ratio and Proportion

Concept:Assume a common multiplier $x$ to represent each salary from the given ratio, then form an equation using the given difference of products.Explanation:Let the salaries of the first, second, and third months be $2x$, $4x$, and $5x$ respectively.Product of the first two months: $2x \times 4x = 8x^2$.Product of the last two months: $4x \times 5x = 20x^2$.The difference between these products is given as $4,80,00,000$.Since the product of the last two months is larger, subtract: $20x^2 - 8x^2 = 12x^2$.Set up equation: $12x^2 = 4,80,00,000$.Divide both sides by $12$: $x^2 = \frac{4,80,00,000}{12} = 40,00,000$.Take the positive square root (salary cannot be negative): $x = \sqrt{40,00,000} = 2000$.Second month salary: $4x = 4 \times 2000 = 8000$.Thus the salary of the second month is $\text{Rs. }8,000$.Answer:$₹ 8,000$