Question

The average of ten number is 7. if every number is multiplied with 12 then the average will be ?

• A. 84
• B. 65
• C. 19
• D. 22

Answer 1

Answer:

A. 84

Effect of Transformations on Average

• A crucial property of averages, often tested in competitive exams, relates to how they change when each number in a set undergoes a uniform transformation.

• General Rule: If every number in a given set of data is subjected to the same arithmetic operation (addition, subtraction, multiplication, or division) by a constant value, the average of the new set of numbers will also be subjected to the same operation by the same constant value.

• This means that whatever uniform change is applied to each individual number, the average of the set will reflect that identical change.

Application to Multiplication

• In the given problem, the initial average of ten numbers is 7.

• Each of these ten numbers is then multiplied by 12.

• According to the general rule explained above, if each number is multiplied by a constant (here, 12), the new average will simply be the old average multiplied by that same constant.

• Therefore, the new average = Old Average × Multiplier = 7 × 12 = 84.