If 45% of a number is 0.9 more than 30% of it, what is the number?

Correct — A. Let the number be n.

Write the gap: 45% of n − 30% of n = 0.9
Subtract the percentages: 15% of n = 0.9
Divide by 0.15: n = 0.9 ÷ 0.15 = 90 ÷ 15 = 6

Check: 45% of 6 = 2.7 and 30% of 6 = 1.8, a gap of 0.9 → option (a)

Why the others are wrong

• (b)
  7 — At 7 the gap is 1.05: 45% of 7 = 3.15 and 30% of 7 = 2.1. The gap is 15% of the number, so it grows with it.
• (c)
  8 — At 8 the gap is 1.2: 45% of 8 = 3.6 and 30% of 8 = 2.4. That is 15% of 8, well above 0.9.
• (d)
  9 — At 9 the gap is 1.35: 45% of 9 = 4.05 and 30% of 9 = 2.7. 0.9 is 10% of 9, not the 15% the gap needs.

Two percentages of the same number differ by a percentage of that number: 45% − 30% = 15% of n. So the stated gap, 0.9, is 15% of n, and n = 0.9 ÷ 0.15.

As a fraction, 15% = 3⁄20, so n = 0.9 × 20⁄3 = 6. Working with the difference saves writing two expressions and solving them.

Key facts

• a% of n − b% of n = (a − b)% of n.
• 15% = 3⁄20 = 0.15.
• 0.9 ÷ 0.15 = 90 ÷ 15 = 6, after multiplying both by 100 to clear the decimals.

Common traps

• Dividing 0.9 by 0.45 or by 0.30: the 0.9 is the gap, so it belongs to the 15% difference.
• Misplacing the decimal: 0.9 ÷ 0.15 is 6, not 0.6 or 60.

No directly related past PYQ was found.