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CAT 2002 — QA Question 9

Change in AverageEasy

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

Answer & solution

  • A

    4

  • 2

  • C

    6

  • D

    8

Solution

Let the Arithmetic Mean of the 10 numbers be x and s be the sum of the remaining 9 numbers.

x+10a+b10=x ...(i)

Interchanging the number ab with ba,

x+10b+a10= x + 1.8 ... (ii)

Subtracting (i) from (ii), we get,

10b + a − (10a + b) = 9(b − a) = 18

b − a = 2

Hence, option (b).

CAT 2002 QA Q9: A boy finds the average of 10 positive integers. Each integer contains two digits. By mistake, the boy interch — Solution | TheCATExam