Question:easy

If 0.06% of a number is 84, then 30% of that number is

Show Hint

Find the number first: divide 84 by 0.0006 to get 140000. Or notice that 30 divided by 0.06 is 500, so just multiply 84 by 500.
Updated On: Jul 17, 2026
  • 25.2
  • 420
  • 42000
  • 2520
Show Solution

The Correct Option is C

Solution and Explanation

Step 1: Use the ratio between the two percentages instead of finding the number.
Both quantities are percentages of the same unknown number, so their values are in the same ratio as the percentages themselves. That means we never actually need the number.

Step 2: Find how many times bigger 30 per cent is than 0.06 per cent.
\[ \frac{30}{0.06} = \frac{3000}{6} = 500 \]
So 30 per cent of the number is exactly 500 times 0.06 per cent of the same number.

Step 3: Scale the known value.
Since 0.06 per cent of the number is 84,
\[ 30\% \text{ of the number} = 84 \times 500 = 42000 \]

Step 4: Confirm the long way.
If you would rather see the number, note that 0.06 per cent is $\frac{6}{10000}$ of the number. So
\[ \frac{6}{10000} \times N = 84 \]
\[ N = \frac{84 \times 10000}{6} = 140000 \]
Then $30\%$ of $140000$ is $\frac{3}{10} \times 140000 = 42000$. Both routes agree, which is a good sign.

Step 5: Why the traps are traps.
2520 equals $84 \times 30$, which mistakes the multiplier 500 for 30. It is what you get if you think "30 per cent is 30 times 1 per cent" and forget that the given percentage is 0.06, not 1.
420 needs the multiplier 5, which would follow only if the first percentage were 6 per cent, that is, if the decimal point were misplaced by two positions.
25.2 is smaller than 84, but since 30 per cent is far larger than 0.06 per cent, the answer must be far larger than 84, so this one can be dropped without any calculation.

Final Answer:
Scaling 84 by the factor 500 gives 42000.
\[ \boxed{42000} \]
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