Question:

One-third of one fourth of a number is 12. Then the number is

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"Of" means multiply, so one-third times one-fourth is one-twelfth. The number is therefore 12 multiplied by 12.
Updated On: Jul 17, 2026
  • 96
  • 144
  • 108
  • 36
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The Correct Option is B

Solution and Explanation

Step 1: Translate the words into symbols.
In maths, the word "of" between fractions means multiply. So "one-third of one-fourth of a number" means
\[ \frac{1}{3} \times \frac{1}{4} \times N \]
where \( N \) is the number we are looking for.

Step 2: Simplify the two fractions into one.
\[ \frac{1}{3} \times \frac{1}{4} = \frac{1}{12} \]
So the phrase simply means one-twelfth of the number.

Step 3: Form the equation and solve.
\[ \frac{N}{12} = 12 \]
Multiply both sides by 12:
\[ N = 12 \times 12 = 144 \]

Step 4: Check the answer by walking the words forward.
One-fourth of 144 is \( \frac{144}{4} = 36 \).
One-third of that 36 is \( \frac{36}{3} = 12 \).
This is exactly the value given in the question, so \( N = 144 \) is correct.

Step 5: Examine the wrong options.
Option (D) 36 is only one-fourth of the number. It is what you get if you stop after the first step of the check above, or if you solve \( \frac{N}{3} = 12 \) alone.
Option (A) 96 comes from adding the fractions as \( \frac{1}{3} + \frac{1}{4} = \frac{7}{12} \) and fumbling, or from multiplying 12 by 8. Neither matches the wording.
Option (C) 108 equals \( 12 \times 9 \), which would fit "one-third of one-third", not "one-third of one-fourth".
Only 144 fits both fractions.

Final Answer:
The number is 144.
\[ \boxed{144} \]
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