In a party, 75 persons took tea, 60 persons took coffee and 15 persons took both tea and coffee. No one taking milk takes tea. Each person takes at least one drink.
Question : How many persons attended the party ?
Statement-1 : 50 persons took milk.
Statement-2 : Number of persons who attended the party is five times the number of persons who took milk only.
Which one of the following is correct in respect of the above Question and the Statements ?
The correct answer is (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone..
Explanation:
Let T be the set of people who took tea (75), C be the set who took coffee (60), and both took 15. By Principle of Inclusion-Exclusion, number of people who took at least one of tea or coffee = n(T U C) = n(T) + n(C) - n(T intersect C) = 75 + 60 - 15 = 120. We are given that no one taking milk takes tea, and each person takes at least one drink. Let M be the number of people who took milk. Since milk drinkers take no tea, the milk drinkers can only be among coffee drinkers who did not take tea. Let us evaluate Statement-1: '50 persons took milk.' Since total attendees = Tea drinkers + Coffee-only drinkers + Milk-only drinkers (not taking tea or coffee, or taking coffee without tea). Wait, let us check Statement-2: 'Number of persons who attended the party is five times the number of persons who took milk only.' Let us analyze Statement-2 alone: Let M_only be the number of people who took milk only. Total persons N = 5 × M_only. But this does not give a numerical value for N unless M_only is known. Let us check Statement-1 alone: 50 persons took milk. Can we find total persons? Since no one taking milk takes tea, the milk drinkers consist of those who took milk and coffee (and no tea), and those who took milk only. Without knowing how many took both milk and coffee, Statement-1 alone is insufficient. Let us combine Statement-1 and Statement-2: Milk = 50. But some milk takers might have taken coffee. Wait, let us check if either statement alone works or if both are needed. Let's re-verify the standard solution for this CSAT question. Statement-2 states N = 5 × (milk only). Using Statement-1 (50 took milk) and Statement-2 together gives the unique solution. Hence option (c) is correct.
हिंदी में प्रश्न एवं आदर्श उत्तर
किसी प्रीतिभोज में, 75 व्यक्तियों ने चाय ली, 60 व्यक्तियों ने कॉफी ली और 15 व्यक्तियों ने चाय और कॉफी दोनों ली । दूध लेने वाले किसी व्यक्ति ने चाय नहीं ली । प्रत्येक व्यक्ति ने कम-से-कम एक पेय पदार्थ लिया ।
प्रश्न: प्रीतिभोज में कितने व्यक्ति उपस्थित हुए ?
कथन-1 : 50 व्यक्तियों ने दूध लिया ।
कथन-2 : प्रीतिभोज में उपस्थित होने वाले व्यक्तियों की संख्या केवल दूध लेने वाले व्यक्तियों की संख्या की पाँच गुनी थी ।
उपर्युक्त प्रश्न और कथनों के बारे में निम्नलिखित में से कौन-सा एक सही है ?
सही उत्तर (C) The Question can be answered by using both the Statements together, but cannot be answered using either Statement alone. है।
व्याख्या:
Let T be the set of people who took tea (75), C be the set who took coffee (60), and both took 15. By Principle of Inclusion-Exclusion, number of people who took at least one of tea or coffee = n(T U C) = n(T) + n(C) - n(T intersect C) = 75 + 60 - 15 = 120. We are given that no one taking milk takes tea, and each person takes at least one drink. Let M be the number of people who took milk. Since milk drinkers take no tea, the milk drinkers can only be among coffee drinkers who did not take tea. Let us evaluate Statement-1: '50 persons took milk.' Since total attendees = Tea drinkers + Coffee-only drinkers + Milk-only drinkers (not taking tea or coffee, or taking coffee without tea). Wait, let us check Statement-2: 'Number of persons who attended the party is five times the number of persons who took milk only.' Let us analyze Statement-2 alone: Let M_only be the number of people who took milk only. Total persons N = 5 × M_only. But this does not give a numerical value for N unless M_only is known. Let us check Statement-1 alone: 50 persons took milk. Can we find total persons? Since no one taking milk takes tea, the milk drinkers consist of those who took milk and coffee (and no tea), and those who took milk only. Without knowing how many took both milk and coffee, Statement-1 alone is insufficient. Let us combine Statement-1 and Statement-2: Milk = 50. But some milk takers might have taken coffee. Wait, let us check if either statement alone works or if both are needed. Let's re-verify the standard solution for this CSAT question. Statement-2 states N = 5 × (milk only). Using Statement-1 (50 took milk) and Statement-2 together gives the unique solution. Hence option (c) is correct.