Question

a boy has to find the average of 25 positive integers. Each integer contains two digits. By mistake, the boy interchanges the digits of one number and finds the average 2.88 less than the real average. What is the difference between the two digits of that number

Answer 1

Answer:

8

Step-by-step explanation:

Let say correct average = x

then sum = 25x

Average calculated = x - 2.88

Sum = 25 (x-2.88) = 25 x - 72

Actual Sum reduced by =   25x - (25x - 72 ) = 72

let say number was  10a + b

it changed to 10b + a

10a + b - (10b + a) = 72

9a - 9b = 72

a-b = 8

Difference between two digits = 8

Answer 2

Answer:

8

Step-by-step explanation:

Let the original number be ab=10a+b

Let the average be y ,i.e,

{(10a+b)+x2+x3+....x25}/25 = y

After interchanging to ba=10b+a, the new average is y-2.88, i.e.,

{ (10b+a)+x2+x3....x25}/25 = y-2.88

On solving above 2 equations:

(10b+a) + 25y-10a-b = 25(y-2.88)

9b-9a = 72

Therefore, a-b=8