Question

A student finds the average of 10
positive integers. Each integer contains two
digits. By mistake, the student interchanges
the digits of one number say ba for ab. Due to
this, the average becomes 1.8 less than the
previous one. What is the difference between
the two digits a and b?​

Answer 1

Answer:

2

Step-by-step explanation:

Let the original number be ab i.e., (10a + b). After interchanging the digits, the new number becomes ba i.e., (10b + a). ... Therefore, the sum of the original 10 numbers will be 10*1.8 more than the sum of the 10 numbers with the digits interchanged. i.e., 10a + b = 10b + a + 18, 9a - 9b = 18, a - b = 2.

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Answer 2

Answer: 2

Step-by-step explanation:

Let A be the sum of first 9 integers

Let the original number be 10y+x

Let the interchanged number be 10x+y

First average = A+10y+x/10

Second average = A + 10x+y / 10

Condition :

A + 10x+y / 10 = A + 10y + x /10 -1.8

= A + 10y+x - 18/10

10 A + 100x + 10y = 10 A + 100y +

10x-18

100x-10x + 10y -100 y = -18

90x-90y = -18

90(x-y)= -18

X-y = 2