## 200 is divided into two parts in such a way that the sixth part of the first and the half part of the second are in the ratio 1:1. What will be the value of the second part?

(A) 150 (B) 125 (C) 75 **(D) 50**

Let’s denote the two parts as \(x\) and \(200 – x\).

According to the given condition, the sixth part of the first part and the half part of the second part are in the ratio 1:1. Mathematically, this can be expressed as:

\[\frac{1}{6} \cdot x = \frac{1}{2} \cdot (200 – x)\]

Now, let’s solve for \(x\):

Multiply both sides of the equation by 6 to get rid of the fraction:

\[x = 3 \cdot (200 – x)\]

Expand the equation:

\[x = 600 – 3x\]

Combine like terms:

\[4x = 600\]

Divide both sides by 4:

\[x = 150\]

Now that we have the value of \(x\), we can find the value of the second part (\(200 – x\)):

\[200 – x = 200 – 150 = 50\]

So, the correct answer is **(D) 50.**