If 30% of m is equal to 18% of n, what is the ratio m: n?

Correct — C. Turn the statement into an equation, then isolate m⁄n.

Write it out: 30⁄100 × m = 18⁄100 × n
Multiply both sides by 100: 30m = 18n
Divide both sides by 30n: m⁄n = 18⁄30
Cancel by 6: m⁄n = 3⁄5

So m : n = 3 : 5 → option (c).

Why the others are wrong

• (a)
  5 : 3 — 5 : 3 is n : m, the ratio turned upside down. The larger percentage (30%) is taken of m, so m must be the smaller number and m : n must be below 1.
• (b)
  2 : 3 — Test it: with m = 2 and n = 3, 30% of 2 = 0.6 but 18% of 3 = 0.54. The two sides are not equal, so 2 : 3 fails the condition.
• (d)
  3 : 2 — 3 : 2 makes m larger than n, which cannot be when 30% of m equals only 18% of n. Check: 30% of 3 = 0.9, but 18% of 2 = 0.36.

When a% of m = b% of n, cross-multiplying gives am = bn, so m : n = b : a. The percentages swap sides.

Here that is 18 : 30, which cancels to 3 : 5.

A sense check follows from the same line: the larger percentage sits on the smaller quantity. If 30% of m only matches 18% of n, m has to be the smaller of the two.

Key facts

• If a% of m = b% of n, then m : n = b : a.
• 18 : 30 = 3 : 5, dividing both terms by their HCF, 6.
• The quantity taken at the larger percentage is the smaller quantity.

Common traps

• Pairing each percentage with its own letter and writing m : n = 30 : 18, which cancels to 5 : 3, the flipped ratio.
• Skipping the five-second check of substituting the ratio back: 30% of 3 = 0.9 = 18% of 5.

No directly related past PYQ was found.