Question:

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

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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
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The Correct Option is C

Solution and Explanation

Step 1: Turn the percentage into a fraction.
Let the number be \( N \). The word "per cent" means "out of a hundred", so
\[ 0.06\% \text{ of } N = \frac{0.06}{100} \times N = 0.0006N \]
Writing the percentage as a plain decimal like this is what keeps the zeros under control.

Step 2: Form the equation and find N.
We are told this equals 84, so
\[ 0.0006N = 84 \]
\[ N = \frac{84}{0.0006} \]
To divide by a small decimal, multiply top and bottom by 10000:
\[ N = \frac{84 \times 10000}{6} = \frac{840000}{6} = 140000 \]
So the number is 140000.

Step 3: Check that N is right.
\[ 0.06\% \text{ of } 140000 = \frac{0.06 \times 140000}{100} = \frac{8400}{100} = 84 \]
This matches the given value, so \( N = 140000 \) is correct.

Step 4: Find 30 per cent of N.
\[ 30\% \text{ of } 140000 = \frac{30}{100} \times 140000 = 0.3 \times 140000 = 42000 \]

Step 5: See why the other options fail.
Option (A) 25.2 is 30 per cent of 84 itself. That treats 84 as the number instead of as 0.06 per cent of it.
Option (B) 420 comes from reading the first percentage as 6 per cent instead of 0.06 per cent, which makes \( N = 1400 \) and 30 per cent of it 420.
Option (D) 2520 is 30 times 84, another shortcut that skips finding \( N \).
Only 42000 follows from the correct value \( N = 140000 \).

Final Answer:
30 per cent of the number is 42000.
\[ \boxed{42000} \]
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