Question

A school has 63 studying Physics, Chemistry and Biology. 33 study Physics,25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study Biology andChemistry, while 8 study both Physics and Biology. Equal number study all three subjectsas those who learn none of the three. How many students study all the three subjects?​

Answer 1

Answer:

3

Step-by-step explanation:

Given  

A school has 63 studying Physics, Chemistry and Biology. 33 study Physics,25 Chemistry and 26 Biology. 10 study Physics and Chemistry, 9 study...

Given a school has 63 students studying physics, chemistry and biology.

33 students study physics

25 students study chemistry

26 students study biology

Now 10 study both physics and chemistry

   9 study both biology and chemistry

  8 study both physics and biology

Now there are 3 students who study all the subjects and also we can say there are 3 students who do not study any of the given subjects.

Number of students who study one among 3 subjects will be

18 + 12 + 9 = 39

We can represent this by venn diagram.

Answer 2

Concept:

It is based on the Venn diagram since it involves mutual subjects in a set.

Given:

Total number of students studying Physics, Chemistry and Biology$=63$

Total number of students studying Physics$=33$

Total number of students studying Chemistry$=25$

Total number of students studying Biology$=26$

Total number of students studying Physics and Chemistry$=10$

Total number of students studying Biology and Chemistry$=9$

Total number of students studying Physics and Biology$=8$

Find:

The total number of students studying all the three subjects.

Solution:

Let x be the number of students who study Physics, Chemistry, and Biology

Total number of students studying Physics and Chemistry$=10-x$

Total number of students studying Physics and Biology$=8-x$

Total number of students studying Chemistry and Biology$=9-x$

Total number of students who studying Physics$=33-(10-x)-x-(8-x)$

$= 33 - 10 + x - x - 8 + x$

$=15+x$

Total number of students who studying Chemistry$= 25 - (10 - x) - x - (9 - x)$

$=25 - 10 + x - x - 9 + x$

$=6+x$

Total number of students who studying Biology$= 26 - (8 - x) - x - (9 - x)$

$= 26 - 8 + x - x - 9 + x$

$=9+x$

If the total number of students studying all the three subjects is equal to the total number of students not studying either of the three subjects

Then,

$(15 + x) + (10 - x) + x + (8 - x) + (6 + x) + (9 - x) + (9 + x ) = 63 - x$

$15 + x + 10 - x + x + 8 - x + 6 + x + 9 - x + 9 + x = 63 - x$

$57 + x = 63 - x$

$x+ x = 63 - 57$

$2x=6$

$x=3$

Hence, the total number of students who study all three subjects is 3.

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