Averageऔसत questions and answersप्रश्न और उत्तर

How average worksऔसत को समझिए

Sum = average × count. Most problems become easy once you write both the old and the new sums.

Replacement: if replacing one person raises the average of n people by d, the new person is n × d heavier (or older) than the person replaced.

Deviation method: pick a convenient base, add up how far each value is from it, and adjust. It avoids big additions.

Each trick says when to use it, why it works and when it fails. Formula tricks are checked by code over their whole range.हर ट्रिक बताती है कि उसे कब इस्तेमाल करें, वह क्यों काम करती है और कब नहीं। सूत्र वाली ट्रिक्स को कोड से उनकी पूरी रेंज पर जाँचा गया है।

Answers and full solutions are shown. Hide them to test yourself first.उत्तर और पूरे हल दिखाए गए हैं। पहले खुद को परखने के लिए इन्हें छिपाइए।

1. Example 1उदाहरण 1 · Averages: replacement and batting average · Easyआसान

   The average weight of 11 players of a kabaddi team increases by 4 kg when a player weighing 50 kg is replaced by a new player. What is the weight of the new player (in kg)?

   1. 75 kg
   2. 85 kg
   3. 94 kg
   4. 118 kg
   Answer:उत्तर: 94 kg

   1. Total weight rises by 11 × 4 = 44 kg.
   2. New player = 50 + 44 = 94 kg.

2. Example 2उदाहरण 2 · Averages: replacement and batting average · Mediumमध्यम

   The average weight of 10 players of a kabaddi team increases by 0.5 kg when a player weighing 46 kg is replaced by a new player. What is the weight of the new player (in kg)?

   1. 38 kg
   2. 51 kg
   3. 56 kg
   4. 64 kg
   Answer:उत्तर: 51 kg

   1. Total weight rises by 10 × 0.5 = 5 kg.
   2. New player = 46 + 5 = 51 kg.

3. Example 3उदाहरण 3 · Averages: replacement and batting average · Hardकठिन

   Shubman scores 73 runs in the 17th innings, and this increases the batting average by 2. What is the batting average after the 17th innings?

   1. 41
   2. 45
   3. 49
   4. 51
   Answer:उत्तर: 41

   1. Old total = 16A; new total = 16A + 73 = 17(A + 2).
   2. So 73 = A + 34, giving A = 39.
   3. New average = 39 + 2 = 41.

4. Example 4उदाहरण 4 · Averages: replacement and batting average · Mediumमध्यम

   The average weight of 10 players of a kabaddi team decreases by 3 kg when a player weighing 70 kg is replaced by a new player. What is the weight of the new player (in kg)?

   1. 20 kg
   2. 30 kg
   3. 40 kg
   4. 50 kg
   Answer:उत्तर: 40 kg

   1. Total weight falls by 10 × 3 = 30 kg.
   2. New player = 70 − 30 = 40 kg.

5. Example 5उदाहरण 5 · Averages: replacement and batting average · Mediumमध्यम

   The average weight of 5 players of a kabaddi team increases by 4 kg when a player weighing 60 kg is replaced by a new player. What is the weight of the new player (in kg)?

   1. 60 kg
   2. 70 kg
   3. 80 kg
   4. 100 kg
   Answer:उत्तर: 80 kg

   1. Total weight rises by 5 × 4 = 20 kg.
   2. New player = 60 + 20 = 80 kg.

6. Example 6उदाहरण 6 · Averages: replacement and batting average · Mediumमध्यम

   The average weight of 10 players of a kabaddi team increases by 2 kg when a player weighing 74 kg is replaced by a new player. What is the weight of the new player (in kg)?

   1. 71 kg
   2. 94 kg
   3. 113 kg
   4. 118 kg
   Answer:उत्तर: 94 kg

   1. Total weight rises by 10 × 2 = 20 kg.
   2. New player = 74 + 20 = 94 kg.

Common mistakesआम गलतियाँ

• Averaging averages of groups with different sizes.
• Forgetting that the count changes when someone joins or leaves.

Frequently asked questionsअक्सर पूछे जाने वाले प्रश्न