Question

Average weight of 11 object is 200kg . If the weight of the new object is also included the average increased by 3 then what is the weight of the new object ?

• A. 200
• B. 250
• C. 236
• D. 320

Answer 1

Answer:

C. 236

Understanding Averages

• The average (or mean) of a set of numbers is calculated by dividing the sum of all the numbers by the total count of numbers.
• The fundamental formula for average is: Average = (Sum of Quantities) / (Number of Quantities).
• This implies that Sum of Quantities = Average × Number of Quantities. This derived formula is crucial for solving many average-related problems in competitive exams.

Step-by-Step Solution

1. Calculate the Initial Total Weight:

   • Initially, there are 11 objects.
   • The average weight of these 11 objects is 200 kg.
   • Using the formula Sum = Average × Number, the total weight of the 11 objects is: 11 × 200 kg = 2200 kg.

2. Determine the New Average and Number of Objects:

   • A new object is included, so the total number of objects becomes 11 + 1 = 12.
   • The average weight increased by 3 kg, so the new average weight is 200 kg + 3 kg = 203 kg.

3. Calculate the New Total Weight:

   • Now, with 12 objects and a new average of 203 kg, the new total weight is: 12 × 203 kg.
   • To calculate 12 × 203: (10 + 2) × 203 = (10 × 203) + (2 × 203) = 2030 + 406 = 2436 kg.

4. Find the Weight of the New Object:

   • The weight of the new object is the difference between the new total weight and the initial total weight.
   • Weight of new object = New Total Weight - Initial Total Weight = 2436 kg - 2200 kg = 236 kg.

Competitive Exam Strategy & Shortcut

• For problems where a new person/item joins or leaves, and the average changes, a powerful shortcut can be used.
• When a new item joins and the average increases:
  Weight of New Object = Old Average + (Increase in Average × New Number of Items)
• Applying this shortcut to the given problem:
  • Old Average = 200 kg
  • Increase in Average = 3 kg
  • New Number of Items = 12 (11 + 1)
  • Weight of New Object = 200 + (3 × 12) = 200 + 36 = 236 kg.
• This shortcut significantly reduces calculation time, which is critical in time-constrained competitive exams.
• Remember the general concept: if an average increases when a new item is added, the new item must be heavier than the old average. Conversely, if it decreases, the new item is lighter.