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?
1). 150
2). 125
3). 75
4). 50
Let the two parts be x and y.
$(\Rightarrow \frac{{\frac{x}{6}}}{{\frac{y}{2}}} = \frac{1}{1})$
$(\Rightarrow \frac{x}{{3y}} = \frac{1}{1})$
$(\Rightarrow \frac{x}{y} = \frac{3}{1})$
Now,
⇒ x + y = 200
Let x = 3a and y = a
⇒ 3a + a = 200
⇒ a = 50
The value of second part = y = 50