The ratio of the present ages of K and M is 4:5. The difference between M's present age and K's age 5 years from now is 3 years. Find (1) the difference between their present ages and (2) the total of their present ages.

Introduction:This question tests using a present-age ratio along with a future-based difference statement. The ratio 4:5 suggests expressing ages as 4x and 5x. The second condition gives an exact numeric difference involving a time shift (K after 5 years). Once x is found, both the present difference and present sum can be computed directly.

Given Data / Assumptions:

• Present ratio K : M = 4 : 5
• Let K = 4x and M = 5x
• Condition: M (present) - (K after 5 years) = 3
• We need present difference (M - K) and present sum (M + K)

Concept / Approach:Use ratio representation. Convert the future difference statement into an equation: 5x - (4x + 5) = 3. Solve for x, then compute difference and sum.

Step-by-Step Solution:Let K = 4x and M = 5xK after 5 years = 4x + 5Given: 5x - (4x + 5) = 35x - 4x - 5 = 3x - 5 = 3 => x = 8K = 4x = 32, M = 5x = 40Present difference = 40 - 32 = 8Present sum = 40 + 32 = 72

Verification / Alternative check:K after 5 years is 37. M present is 40. Difference 40 - 37 = 3 matches the given statement. So both ages are correct, hence difference and sum are correct.

Why Other Options Are Wrong:10 and 60: implies ages 25 and 35, but 35 - (25+5) = 5, not 3.12 and 84: implies larger x which breaks the 3-year condition.16 and 65: inconsistent because with ratio 4:5, sum must be 9x (a multiple of 9).6 and 54: gives x=6, then 5x - (4x+5) = 6 - 5 = 1, not 3.

Common Pitfalls:Using present difference instead of the future-shifted difference in the equation.Adding 5 years to M instead of only to K.Forgetting the question asks for both difference and total.

Final Answer:8 years and 72 years