Question

Given A = x+y² +z³. If x increases by 6300%, y increases by 700% and z increases by 300%, then 3 what is the percentage increase in the value of A?

• A. 12
• B. 18
• C. 26
• D. 33
• E. 63

Answer 1

Answer: (E)

To solve this problem, we need to find the percentage increase in the value of \(A = x + y^2 + z^3\). Initially, let's denote the original values of \(x\), \(y\), and \(z\) as \(x_0\), \(y_0\), and \(z_0\) respectively. The initial value of \(A\) is:

1. Initial Value of \(A\): \(A_0 = x_0 + y_0^2 + z_0^3\). 

Given percentage increases, we have:

• \(x\) increases by 6300%, so the new value of \(x\) is: \(x_1 = x_0 + \frac{6300}{100} \times x_0 = 64x_0\).
• \(y\) increases by 700%, so the new value of \(y\) is: \(y_1 = y_0 + \frac{700}{100} \times y_0 = 8y_0\).
• \(z\) increases by 300%, so the new value of \(z\) is: \(z_1 = z_0 + \frac{300}{100} \times z_0 = 4z_0\).

Now, calculate the new value of \(A\):

1. New Value of \(A\): \(A_1 = x_1 + y_1^2 + z_1^3 = 64x_0 + (8y_0)^2 + (4z_0)^3\).
2. \(A_1 = 64x_0 + 64y_0^2 + 64z_0^3\).

The percentage increase in the value of \(A\) is given by:

• Percentage Increase: \(\frac{{A_1 - A_0}}{A_0} \times 100 = \frac{{64x_0 + 64y_0^2 + 64z_0^3 - (x_0 + y_0^2 + z_0^3)}}{x_0 + y_0^2 + z_0^3} \times 100\)

Simplifying further:

1. \(\frac{{63x_0 + 63y_0^2 + 63z_0^3}}{x_0 + y_0^2 + z_0^3} \times 100 = 63\%\).

Therefore, the correct percentage increase in the value of \(A\) is 63%.

The correct answer is 63.