If 25% of three sevenths of 26% of a number is equal to 145.5, what is the approximate value of that number?

Introduction / Context:
This question involves several percentage and fraction operations applied successively to an unknown number. It tests whether you can correctly translate the language into a mathematical expression and then solve for the original number, handling decimal values carefully.

Given Data / Assumptions:

• Let the unknown number be N.• First we take 26% of N.• Then we take three sevenths of that result.• Then we take 25% of that new value.• The final value obtained is 145.5.

Concept / Approach:
Percentages such as 25% and 26% can be written as fractions. The phrase three sevenths describes another fraction applied to the intermediate result. Multiplying all these fractions together gives one overall factor times N, which we set equal to 145.5. Solving this equation yields the required number.

Step-by-Step Solution:
Step 1: Twenty six percent of N = (26/100) * N.Step 2: Three sevenths of that = (3/7) * (26/100)N.Step 3: Twenty five percent of the new result = (25/100) * (3/7) * (26/100)N.Step 4: Combine the fractions: numerator = 25 * 3 * 26 = 1950, denominator = 100 * 7 * 100 = 70000.Step 5: Overall factor = 1950/70000, which simplifies to 39/1400.Step 6: So (39/1400)N = 145.5.Step 7: Solve for N: N = 145.5 * (1400/39).Step 8: Evaluate this product to obtain N approximately equal to 5223.08.Step 9: Among the given options, 5223 is the closest and therefore the correct choice.

Verification / Alternative check:
Check by substituting N = 5223. Compute 26% of 5223, then three sevenths of that, and then 25% of the result. The final value comes out very close to 145.5, with a small rounding difference due to decimal approximations, which is acceptable in typical multiple choice settings.

Why Other Options Are Wrong:
Values 4987, 5784 and 4741 produce final results that are significantly farther from 145.5 when the same sequence of operations is applied. They do not satisfy the equation even approximately.

Common Pitfalls:
Candidates often misplace the percentage factors or apply them in the wrong order, which changes the overall fraction drastically. Another error is forgetting that 145.5 already includes a decimal and rounding too early in the calculations.

Final Answer:
The approximate value of the number is 5223.