Twenty one is equal to 35 percent of a certain number. Based on this information, find that original number.

Introduction / Context:
This problem reverses the usual direction of percentage questions. Instead of asking for a percentage of a known number, it gives the result of a percentage and asks you to find the original number. This is a common pattern in aptitude tests and helps you practice solving simple equations involving percentages.

Given Data / Assumptions:

• 21 is given as 35 percent of some unknown number N.
• Mathematically, 21 = 35 percent of N.
• We need to find the value of N that satisfies this relation.

Concept / Approach:
If p percent of N equals a known value V, then (p / 100) * N = V. To find N, rearrange this to N = (V * 100) / p. Here, p = 35 and V = 21. Careful handling of the fraction and cancellation makes the calculation easy and exact.

Step-by-Step Solution:
Step 1: Write the percentage equation: (35 / 100) * N = 21. Step 2: Rearrange to solve for N: N = (21 * 100) / 35. Step 3: Simplify the fraction 100 / 35. Divide numerator and denominator by 5 to get 20 / 7. Step 4: Now N = 21 * (20 / 7). Step 5: Simplify 21 / 7 = 3, so N = 3 * 20 = 60.

Verification / Alternative check:
Check the answer by computing 35 percent of 60: (35 / 100) * 60 = 0.35 * 60 = 21. Since this matches the given value, the solution is verified as correct.

Why Other Options Are Wrong:

• 85 would give 35 percent of 85 as 29.75, not 21.
• 300 would give 105 as 35 percent, which is far too large.
• 21 would imply 35 percent of 21 equals 21, which is impossible since any proper percentage less than 100 is smaller than the original number.

Common Pitfalls:
A common error is to multiply 21 by 0.35 instead of dividing by 0.35. Remember that 21 is the percentage result, not the original base. Always set up the equation carefully and solve for the unknown base when reversing a percentage calculation.

Final Answer:
The original number is 60.