Fractional Calculation: Finding 40% of a Number

Let the unknown number be represented by '$x$'.

Step 1: Formulate the Equation

The problem states that "Two-fifth of seven-seventeenth of three-fifth of a number is 84". This translates to the following equation:

$ \frac{2}{5} \times \frac{7}{17} \times \frac{3}{5} \times x = 84 $

Step 2: Calculate the Product of Fractions

Multiply the given fractions together:

$ \frac{2 \times 7 \times 3}{5 \times 17 \times 5} = \frac{42}{425} $

The equation simplifies to:

$ \frac{42}{425} \times x = 84 $

Step 3: Solve for the Number (x)

To isolate '$x$', rearrange the equation:

$ x = 84 \times \frac{425}{42} $

Perform the calculation:

$ x = 2 \times 425 $

$ x = 850 $

The value of the number is 850.

Step 4: Calculate 40% of the Number

The final step is to find 40% of the number '$x$' (which is 850).

Convert 40% to a decimal or fraction: $40\% = \frac{40}{100} = 0.4$.

Calculate 40% of 850:

$ 0.4 \times 850 $

Alternatively, using fractions:

$ \frac{40}{100} \times 850 = \frac{2}{5} \times 850 $

$ = \frac{2 \times 850}{5} = 2 \times 170 $

$ = 340 $

Thus, 40% of the number is 340.