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.