Question

In a group of friends, 50% are engineers, 35% are cricketers and 40% are married. The percentage of friends who are engineers as well as cricketers but not married is equal to the percentage of friends who are both engineers and cricketers as well as married. Also, the number of married cricketers who are not engineers is equal to the number of married engineers who are not cricketers. The percentage of friends who are married, but are neither cricketers nor engineers, is 25%. Q. What is the percentage of friends who are both cricketers and engineers as well as married??

Answer 1

Answer:

Percentage of friends who are both cricketers and engineers as well as married = 5 %

Step-by-step explanation:

Let us assume that there are 100 friends in total.

n(E U C U M) = 100

( It is assumed that there are no members who are not engineers, not cricketers , not married)

Let E denote Engineers

C denote Cricketers

M denote Married

n(E) = 50 ; n(C) = 35 ;  n(M) = 40 ;

Friends who are engineers as well as cricketers but not married is equal to the percentage of friends who are both engineers and cricketers as well as married.

So, n(E ∩ C) = E and C but not M +  n(E ∩ C ∩ M)

Let  n(E ∩ C ∩ M) = x

So,  n(E ∩ C) = 2x

Married cricketers who are not engineers is equal to the number of married engineers who are not cricketers.

Let Married cricketers who are not engineers be 'y'.

E and M but not C = C and M but not E = y

Friends who are married, but are neither cricketers nor engineers = 25

n(M) = n( M and not E and not C) + x + 2y

40 = 25 + x + 2y

y = (15 - x) / 2

We know that the Venn diagram formula is:

n(E U C U M) = n(E) + n(C) + n(M) - n(E ∩ C) - n(E ∩ M) - n(C ∩ M)  + n(E ∩ C ∩ M)

100 = 50 + 35 + 40 - 2x - (x+y) - (x+y) + x

100  = 125 - 3x - 2y

3x + 2 / 2 * (15 - x) = 25

2 x = 10

x = 5

So, percentage of friends who are both cricketers and engineers as well as married = n(E ∩ C ∩ M) = 5 %