$ ext{If } \frac{x}{\sqrt{1.96}} = 400 ext{, then the value of 'x' is :}$

Question

$	ext{If } \frac{x}{\sqrt{1.96}} = 400 	ext{, then the value of 'x' is :}$

Accepted Answer

To solve the problem and justify why Option 2 is correct, we need to find the value of 'x' given the equation:

$$
\frac{x}{\sqrt{1.96}} = 400
$$

First, let's simplify the equation:

1. Calculate $\sqrt{1.96}$:
   $$
   \sqrt{1.96} = 1.4
   $$

2. Substitute $\sqrt{1.96}$ with 1.4 in the equation:
   $$
   \frac{x}{1.4} = 400
   $$

3. Solve for 'x' by multiplying both sides of the equation by 1.4:
   $$
   x = 400 \times 1.4
   $$

4. Calculate the product:
   $$
   x = 560
   $$

Therefore, the value of 'x' is 560, which corresponds to Option 2.

Now, let's explain why each of the other options is incorrect:

- **Option 1: 532.4**  
  This option is incorrect because when you multiply 400 by 1.4, the result is 560, not 532.4. The calculation does not support this value.

- **Option 3: 440**  
  This option is incorrect because multiplying 400 by 1.4 gives 560, not 440. The arithmetic operation clearly shows that 440 is not the correct result.

- **Option 4: 480**  
  This option is incorrect because the multiplication of 400 by 1.4 results in 560, not 480. The calculation confirms that 480 is not the correct value.

In conclusion, the correct answer is Option 2, which is 560, as it is the only option that satisfies the equation $\frac{x}{\sqrt{1.96}} = 400$.