Solve for the number: Four-fifths (4/5) of a number exceeds two-thirds (2/3) of the same number by 8. What is the number?

Introduction / Context:
Many aptitude questions compare two fractional parts of the same unknown and provide the difference between them. The key is to set up a linear equation using the difference of fractions and solve cleanly. Here, 4/5 of a number is greater than 2/3 of that number by 8 units.

Given Data / Assumptions:

• Let the number be n (real and positive).
• (4/5)n − (2/3)n = 8.
• We are to find n.

Concept / Approach:
Compute the difference of the two fractions as a single fraction of n, then equate to 8. Solving for n requires only basic fraction arithmetic and cross-multiplication. Using least common multiples for denominators speeds up the calculation.

Step-by-Step Solution:

Verification / Alternative check:
Check directly: 4/5 of 60 is 48; 2/3 of 60 is 40; 48 − 40 = 8. The condition is satisfied exactly.

Why Other Options Are Wrong:
30, 90, and 48 do not satisfy the given difference when substituted. “None of these” is unnecessary since a valid solution exists.

Common Pitfalls:
Subtracting the fractions incorrectly (e.g., 4/5 − 2/3 = 2/5, which is wrong); forgetting to multiply by the reciprocal when isolating n.

Final Answer:
60