Question

11. In a group of women, 45% drink tea, 35%
drink coffee and 25% of the women drink both
tea and coffee.
(i) Find the percentage of women who drink
neither tea nor coffee.
(ii) If the number of women who drink tea
and/or coffee is 165, find the number of
women in the group.​

Answer 1

Answer:

45% drink neither tea nor coffee

300 women in the group.

Explanation:

given

45% drink tea let n(a)=45

35%drink coffee let n(b)=35

25% drink both let n(anb)=25

1. we know that

total n(aUb)=n(a)+n(b)-n(anb)

=45+35-25

=80-25

=55

so we know that 55% drink either tea or coffee or both but we need to find the no. of women who don't drink either.

i.e n(aUb)'=100-55=45%

therefore answer of the first part is 45% women don't drink either.

2. for part two we know 55% drink either or both drinks .

therefore

given 55% of total women drink either or both drinks

i.e (55×T)/100=165 (T is the total no. of women in the group.)

therefore T=165×100/55

T=300

therefore there are total 300 women in the group.