There are 917 students in a college out of whom 535 are boys. In the diagram, the triangle represents 134 students studying in English medium and the circle represents 279 students in science stream. Girls are represented by the rectangle. Partial information regarding the break up of the students and their choice of medium and stream is included in the diagram. Calculate how many boys are studying in science stream in the English medium.
Let's check the diagram carefully.
Given
Total students $=917$
Boys $=535$
Therefore girls (rectangle) $=917-535=382$
The numbers shown are:
- Rectangle only $=247$
- Triangle $\cap$ Rectangle only $=24$
- Circle $\cap$ Rectangle only $=94$
- Triangle only $=52$
- Circle only $=137$
Let
- Common region (Triangle $\cap$ Circle $\cap$ Rectangle) $=x$
- Triangle $\cap$ Circle but outside Rectangle $=y$
Using Rectangle (Girls)
$247+24+94+x=382$
$x=17$
Using Circle (Science stream)
Total science students $=279$
$137+94+17+y=279$
$248+y=279$
$y=31$
Required
"Boys studying science stream in English medium"
= Triangle $\cap$ Circle but outside Rectangle
= $y$
Therefore,
$\boxed{31}$
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