Three fifths of my current age is equal to five sixths of the current age of one of my cousins. My age ten years ago will be equal to his age four years from now. What is my current age in years?

Introduction / Context:
This is a multi condition age puzzle involving fractions of ages and a comparison between past and future ages. The question tests your ability to handle rational relationships (fractions) as well as time shifts simultaneously. It is more challenging than simple ratio or difference based age problems because you must form and solve two equations with two unknowns, each equation containing fractional coefficients.

Given Data / Assumptions:

• Three fifths of my current age equals five sixths of my cousin current age.
• My age ten years ago will be equal to my cousin age four years from now.
• We have to find my present age in years.
• Both people ages increase linearly and are assumed to be whole numbers in the final answer.

Concept / Approach:
This problem is best approached by using algebra. Define one variable for my current age and another for the cousin current age. The fraction statement gives one linear equation relating these variables. The comparison between my age ten years ago and cousin age four years hence gives another linear equation. Solving these two equations simultaneously yields the numerical value for my present age. Working carefully with fractions is crucial to avoid arithmetic errors. It is often helpful to clear denominators by multiplying both sides of the equation by a common multiple such as 30.

Step-by-Step Solution:
Step 1: Let my current age be M years and my cousin current age be C years. Step 2: From the fraction condition, (3/5) × M = (5/6) × C. Step 3: Multiply both sides by 30, a common multiple of 5 and 6, to avoid fractions. This gives 18M = 25C, so C = (18/25) × M. Step 4: The second condition says that my age ten years ago, M − 10, is equal to my cousin age four years from now, C + 4. Step 5: Substitute C = (18/25) × M into M − 10 = C + 4 and solve the resulting equation to obtain M = 50. Step 6: Therefore my current age is 50 years.

Verification / Alternative check:
Check the relationships using M = 50 years. Then my cousin age is C = (18/25) × 50 = 36 years. Now compute three fifths of my age: (3/5) × 50 = 30, and five sixths of my cousin age: (5/6) × 36 = 30. These are equal, so the first condition is satisfied. Next check the past and future condition: my age ten years ago was 40 years, and my cousin age four years from now will be 36 + 4 = 40 years. These also match, so both conditions hold exactly, confirming that 50 is the correct current age.

Why Other Options Are Wrong:
Option 60: If my age were 60, the cousin age from the first equation would not produce a match with the second condition when tested.
Option 55: Substituting 55 in place of M fails to satisfy one or both equations, so it cannot be correct.
Option 45: This value also leads to inconsistent results between the fraction condition and the age comparison condition.
Option 40: If M is 40, three fifths of my age is 24, and this does not align with a cousin age that satisfies the second condition.

Common Pitfalls:
Students often mix up which age goes with which fraction or forget to align the past and future ages correctly. Another frequent mistake is to make algebraic slips when clearing denominators, for example by multiplying only one side or not multiplying every term. A good strategy is to write both equations clearly, choose a convenient common multiple to eliminate fractions, and only then proceed to substitution. Always verify both conditions at the end with the found ages to ensure the answer is fully consistent.

Final Answer:
My current age is 50 years.