Question

If 40% of \(\frac{2}{5}\)th of a number is 24, find the value of the number.

• A. 200
• B. 100
• C. 250
• D. 150

Hint:

Combine 40% and \(\frac{2}{5}\) into one multiplier (0.16) and divide 24 by it.

Answer 1

The Correct Option is D

Step 1: Set up the equation.
Let the number be \(N\). "40% of \(\frac{2}{5}\)th of a number" means we first take \(\frac{2}{5}\) of \(N\), then take 40% of that result. Written as one equation:
\[ 40\% \times \frac{2}{5} \times N = 24 \]

Step 2: Convert the percentage to a fraction.
\[ 40\% = \frac{40}{100} = 0.4 \]
So the equation becomes
\[ 0.4 \times \frac{2}{5} \times N = 24 \]

Step 3: Combine the two multipliers into a single coefficient.
\[ \frac{2}{5} = 0.4 \]
\[ 0.4 \times 0.4 = 0.16 \]
So
\[ 0.16N = 24 \]

Step 4: Solve for \(N\).
\[ N = \frac{24}{0.16} = 150 \]

Step 5: Verify and eliminate other options.
Check: \(\frac{2}{5}\) of 150 is 60, and 40% of 60 is 24, which matches. Testing option (a) 200 gives \(\frac{2}{5}\) of 200 = 80, and 40% of 80 = 32, not 24, so it fails. Similarly options (b) and (c) do not give 24 either.

Final Answer:
The number is 150.
\[ \boxed{150} \]