25 percent of all wise people are nice and half of all nice people are wise. Further 25 percent of all people are neither wise nor nice, what percentage of all the people are both wise and nice?
Answers
15% of all the people are both wise and nice
Step-by-step explanation:
Let say total People = 4P
25 percent of all people are neither wise nor nice
=> people who are neither wise nor nice = P
Nice People = N
Wise People = W
Total People = N + W - (Nice ∩ Wise) + neither wise nor nice
=> 4P = N + W - N ∩ W + P
=> 3P = N + W - N ∩ W
25 percent of all wise people are nice
=> N ∩ W = W/4 ( Nice & Wise Both)
half of all nice people are wise.
=> N ∩ W = N/2 ( Nice & Wise Both)
Equating Both
=> W/4 = N/2
=> W = 2N
3P = N + W - N ∩ W
=> 3P = N + 2N - N/2
=> 3P = 5N/2
=> N/2 = 3P/5
=> N/2 = 0.6P
Nice & Wise Both = N/2 = 0.6P
percentage of all the people are both wise and nice = (0.6P/4P) * 100
= 15 %
15 % of all the People are Both Nice & Wise
Additional Info
Wise People = 60 %
Nice People = 30 %
Nice & Wise People = 15 %
Neither Nice nor Wise = 25 %