a) 100

b) 150

c) 200

d) 400

Correct answer is: c) 200

Explanation

Let,
The total number of boys 'x'.
According to the question,
Boys passed in spelling =\left(x\times\large\frac{90}{100}\right)
\rightarrow\large\frac{90x}{100}
\rightarrow 0.90x
And,
Boys passed in Arithmetic =\left(x\times\large\frac{85}{100}\right)
\rightarrow\large\frac{85x}{100}
\rightarrow 0.85x
Now,
Boys passed in both subject =
{(Boys passed in spelling + Boys passed in Arithmetic) − Total number of boys}
\rightarrow\{\left(0.90x+0.85x\right)-x\}
\rightarrow\left(1.75x-x\right)
\rightarrow 0.75x
So that,
0.75x=150
\rightarrow x=\large\frac{150}{0.75}
\rightarrow x=\large\frac{150\times100}{75}
\rightarrow x=200
\therefore The total number of boys =200.
Ans: 200 is the total number of boys.