Let number of boys = x
Let number of girls = y and number of students for history x + y = 48
Question => what percentage of girls do not like to study history
Let number of girls who do not like history = g
$$percentage\ of\ \left(g\right)=\frac{g}{y}\cdot\frac{100}{1}$$
Number of girls who like to study history = ( total number of girls) - ( girls who do not like to study history)
= y - g
Statement 1 => one-third of the boys in the class like to study history
Students who like to study history = ( boys who like history ) + ( girls who like history )
16 = ( boys who like history ) + y - g
Boys who like history = 16 - y + g
This statement gives the information that boys who like to study history take up 1/3 of total boys in the class
Therefore, boys who like history = 1/3 ( of number of boys ) where boys who like to study history = 16 - y + g and the total number of boys in the class => x = 48 - y
16 - y + g = 1/3 ( 48 - y )
$$16-y+g=\frac{48-y}{3}$$
3 ( 16 - y + g ) = 48 - y
48 - 3y + 3g = 48 - y
48 + 3g = 48 - y + 3y
3g = 48 + 2y - 48
$$\frac{3g}{3}=\frac{2y}{3}$$
g = 2y/3 (divide both sides by y)
$$\frac{g}{y}=\frac{2}{3}=>g\ =2\ and\ y\ =3$$
From question stem, percentage of (g) = g/y * 100
where q/y = 2/3
Percentage of girls who do not like to study history = 2/3%
Statement 1 is SUFFICIENT
Statement 2 => The number of girls who like history is 50% of the number of girls who do not like history
=> y - g = 50% of g
$$y-g=\frac{150}{100}\cdot g$$
$$y-g=\frac{1}{2}g$$
y - g = 1/2 * g
y - g = g/2
2 ( y - g ) = g
2y - 2g = g
2y = g + 2g
$$\frac{2y}{3}=\frac{3y}{3}$$
$$g=\frac{2y}{3}$$
g/y = 2/3
From question stem % of g = g/y * 100
Where g/y = 2/3
% of g = 2/3%
Statement 2 is SUFFICIENT
Since each statement alone is SUFFICIENT
Answer = option D
