Question

In an office, the number of persons who take tea is twice the number of persons who take only coffee. The number of persons who take coffee is twice the number of persons who take only tea.

Consider the following statement:

1. The sum of the number of persons who take either tea or coffee or both is four times the number of persons who take both coffee and tea.

2. The sum of the number of persons who take only coffee and those who take only tea is twice the number of persons who take both tea and coffee.

Which of the statement(*) given above is/are correct?

(a) 1 only (b) 2 only (c) Both 1 and 2 (d) Neither 1 nor 2

Answer 1

(b) Let the no. of only tea takers be x, number of only coffee takers be y and number of both tea and coffee takers be z.

Now,

x + z = 2y . ...(i)

y + z = 2x ....(ii)

Solving (i) and (ii), we get

x = y = z

x + y + z = z + z + z = 3z

Thus, statement 1 is not correct.

Also, x + y = z + z = 2z

Thus, statement 2 is correct.