Question 52

x = 4

To solve the proportion 0.1:10::x:400, we can cross-multiply to find that 0.1 times 400 equals 10 times x, leading us to calculate that x equals 4.

A) 25

Option A is incorrect because substituting 25 for x in the proportion yields 0.1:10::25:400, which does not satisfy the equality. Cross-multiplying results in 0.1 * 400 = 40, while 10 * 25 = 250, making this option invalid.

B) 5

Option B is also incorrect. If we substitute 5 for x, the proportion becomes 0.1:10::5:400. Cross-multiplying gives us 0.1 * 400 = 40, but 10 * 5 = 50, which does not hold true, indicating that this option does not satisfy the proportion.

C) 50

Option C is not correct either. Replacing x with 50 results in the proportion 0.1:10::50:400. Upon cross-multiplication, we find that 0.1 * 400 = 40, while 10 * 50 = 500, which shows that this option fails to create a valid equality.

D) 4

Option D is the correct answer. Substituting 4 for x gives us the proportion 0.1:10::4:400. Cross-multiplying results in 0.1 * 400 = 40, and 10 * 4 = 40, confirming that both sides of the proportion are equal.

Conclusion

The correct answer is definitively 4, as it maintains the equality in the given proportion. Options A, B, and C fail to satisfy the proportion when evaluated, confirming that they are incorrect. Thus, option D is the only viable solution in this context.