Three-fourth of two-third of a number is 782. What is three-fifth of one-fourth of the same number ?

Answer

To solve the problem step by step, we will first determine the unknown number based on the information given and then find the required fraction of that number.

### Step 1: Define the variable
Let the unknown number be \( x \).

### Step 2: Calculate two-thirds of the number
Two-thirds of the number can be expressed as:
\[ \frac{2}{3} \times x = \frac{2x}{3} \]

### Step 3: Calculate three-fourths of two-thirds of the number
Now, we need to find three-fourths of two-thirds of the number:
\[ \frac{3}{4} \times \frac{2x}{3} = \frac{3 \times 2x}{4 \times 3} = \frac{2x}{4} = \frac{x}{2} \]

### Step 4: Set up the equation
According to the problem, this value equals 782:
\[ \frac{x}{2} = 782 \]

### Step 5: Solve for \( x \)
To find \( x \), multiply both sides of the equation by 2:
\[ x = 782 \times 2 = 1564 \]

### Step 6: Calculate one-fourth of the number
Now, we need to find one-fourth of the number:
\[ \frac{1}{4} \times x = \frac{1}{4} \times 1564 = \frac{1564}{4} = 391 \]

### Step 7: Calculate three-fifths of one-fourth of the number
Finally, we need to find three-fifths of one-fourth of the number:
\[ \frac{3}{5} \times 391 = \frac{3 \times 391}{5} = \frac{1173}{5} = 234.6 \]

### Final Answer
Thus, three-fifth of one-fourth of the same number is:
\[ \boxed{234.6} \]

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