Question:easy
If 40% of \(\frac{2}{5}\)th of a number is 24, find the value of the number.
If 40% of \(\frac{2}{5}\)th of a number is 24, find the value of the number.
Show Hint
Combine 40% and \(\frac{2}{5}\) into one multiplier (0.16) and divide 24 by it.
Updated On: Jul 15, 2026
- 200
- 100
- 250
- 150
Show Solution
The Correct Option is D
Solution and Explanation
Step 1: Undo the outer operation first instead of combining the multipliers.
Let the number be $N$, and let $M = \frac{2}{5}$ of $N$. The problem says 40% of $M$ is 24:
\[ 0.4 \times M = 24 \]
Step 2: Solve for $M$ first.
\[ M = \frac{24}{0.4} = 60 \]
So $\frac{2}{5}$ of the number is 60.
Step 3: Now undo the inner operation to find $N$.
Since $\frac{2}{5} \times N = 60$, multiply both sides by the reciprocal $\frac{5}{2}$:
\[ N = 60 \times \frac{5}{2} \]
Step 4: Work out the multiplication.
\[ N = \frac{60 \times 5}{2} = \frac{300}{2} = 150 \]
Step 5: Double check by reversing the whole chain.
$\frac{2}{5}$ of 150 is 60, and 40% of 60 is 24, which matches the given information exactly. Working backward this way, one operation at a time, avoids any error in multiplying the two fractions together at once.
\[ \boxed{150} \]
Let the number be $N$, and let $M = \frac{2}{5}$ of $N$. The problem says 40% of $M$ is 24:
\[ 0.4 \times M = 24 \]
Step 2: Solve for $M$ first.
\[ M = \frac{24}{0.4} = 60 \]
So $\frac{2}{5}$ of the number is 60.
Step 3: Now undo the inner operation to find $N$.
Since $\frac{2}{5} \times N = 60$, multiply both sides by the reciprocal $\frac{5}{2}$:
\[ N = 60 \times \frac{5}{2} \]
Step 4: Work out the multiplication.
\[ N = \frac{60 \times 5}{2} = \frac{300}{2} = 150 \]
Step 5: Double check by reversing the whole chain.
$\frac{2}{5}$ of 150 is 60, and 40% of 60 is 24, which matches the given information exactly. Working backward this way, one operation at a time, avoids any error in multiplying the two fractions together at once.
\[ \boxed{150} \]
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