A survey show that in a city that 63% of the citizens like tea where as 76% like coffee. If x% like both tea and coffee, then

Let the population of the city be 100Let A denote the set of citizens who like tea and B denote the set of citizens who like coffee.∴ n(A)=63 and n(B)=76∴ n(A∪B)=n(A)+n(B)− n(A∩B) andn(A∪B)≤100⇒63+76−n(A∩B) ≤100⇒63+76−n(A∩B)≤100⇒39≤n(A∩B) ≤(1)Also n(A∩B)≤n(A) and n(A∩B) ≤n(B)⇒nA∩B≤63 and nA∩B≤76⇒nA∩B≤63 →(2)From (1) and (2) : 39≤nA∩B≤63⇒39≤x≤63