Multiple choice

Find the correct relationship between the given quantities: Quantity I: The present average weight of 15 students of a class, if earlier, the average weight of 14 students, each weighing 1.5 kg more then the present weight, was 56kg and now a new boy weighing 50 kg was added as the 15th student. Quantity II: The number of ways 3 people from 3 men and 3 women can be selected and arranged on 3 chairs such that atmost one of them is a woman. मात्रा I: एक कक्षा में वर्तमान में 15 छात्रों का औसत भार, यदि पहले, 14 छात्रों का औसत भार, वर्तमान भार से प्रत्येक के भार से 1.5 कि.ग्रा. अधिक, 56 किग्रा था और नया लड़का जिसका वज़न 50 कि.ग्रा है को 15वें छात्र के रूप में जोड़ा गया। मात्रा II: तरीकों की संख्‍या जिसे 3 आदमी और 3 औरतों में से 3 लोगों द्वारा चुना जा सकता है और इन 3 कुर्सियों में से अधिकतम पर एक औरत है।

  1. Quantity II > Quantity I मात्रा II > मात्रा I

  2. Quantity I ≥ Quantity II मात्रा I ≥ मात्रा II

  3. Quantity I > Quantity II मात्रा I > मात्रा II

  4. Quantity I ≤ Quantity II मात्रा I ≤ मात्रा II

  5. Quantity I = Quantity II or relationship cannot be established मात्रा I = मात्रा II या कोई संबंध स्थापित नहीं किया जा सकता
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A Correct answer
Explanation

Quantity I: 14 students at 56 kg average were each 1.5 kg heavier than present. Current weight of these 14 students: (56 - 1.5) × 14 = 54.5 × 14 = 763 kg. Adding 50 kg boy: 763 + 50 = 813 kg. Present average: 813 ÷ 15 = 54.2 kg. Quantity II: Select 3 people from 3 men and 3 women with at most 1 woman. Cases: (i) All 3 men: 3C3 = 1 way, (ii) 2 men + 1 woman: 3C2 × 3C1 = 3 × 3 = 9 ways. Total selection: 10 ways. Arrangement on 3 chairs: 10 × 3! = 10 × 6 = 60 ways. Quantity II (60) > Quantity I (54.2).

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