Question

In a group of 100 people, 65 like to play cricket, 40 like to play tennis and 55 like to play volleyball. All of them like to play at least one of three games. If 25 like to play both cricket and tennis,24 like to play tennis and volleyball and 22 like to play both cricket and volley ball then, (i) How many like to play all the three games? (ii) How many like to play cricket only? (iii) How many like to play tennis only?
pls write steps too​

Answer 1

Answer:

Let those who like to play cricket be x, those who like to play tennis be y and who play volleyball be z.

x+y=25; x=25-y....1

y+z=24; y=24-z....2

x+z=22; x=22-z....3

From 1 and 3

x=25-y=22-z

25-y=22-z

Now, from 2,

25-(24-z)=22-z

25-24+z=22-z

1+z=22-z

z+z=22-1

2z=20

z=20/2=10

Now, substituting value of z in 2..

y=24-z=24-10=14

Now, x=25-y

=25-14=11

Answer 2

Answer:

Let those who like to play cricket be x, those who like to play tennis be y and who play volleyball be z.

x+y=25; x=25-y....1

y+z=24; y=24-z....2

x+z=22; x=22-z....3

From 1 and 3

x=25-y=22-z

25-y=22-z

Now, from 2,

25-(24-z)=22-z

25-24+z=22-z

1+z=22-z

z+z=22-1

2z=20

z=20/2=10

Now, substituting value of z in 2..

y=24-z=24-10=14

Now, x=25-y

=25-14=11

Step-by-step explanation: