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The average of 10 two-digit positive integers is Z. However, one number AB is taken as BA, then the average increases to Z + 2.7. What is the value of |B - A|?
- a)1
- b)2
- c)3
- d)4
Correct answer is option 'C'. Can you explain this answer?
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Given:
- Average of 10 two-digit positive integers = Z
- Average increases to Z+2.7 when one number AB is taken as BA
To find: |B - A|
Solution:
Let's assume that the sum of original 10 two-digit positive integers is S.
So, we can say that:
- Average of 10 two-digit positive integers = S/10 = Z
- Sum of 10 two-digit positive integers = S
When we interchange the digits of one number AB and make it BA, the sum of the 10 two-digit positive integers will increase by (BA - AB) = 9(B - A).
So, the sum of the 10 two-digit positive integers after this interchange will be (S + 9(B - A)).
Now, we know that:
- Average of 10 two-digit positive integers after the interchange = (S + 9(B - A))/10 = Z + 2.7
Substituting the value of Z from the first equation, we get:
(S + 9(B - A))/10 = (S/10) + 2.7
Simplifying this equation, we get:
9(B - A) = 27
B - A = 3
Therefore, the value of |B - A| is 3, which is option (c).
Hence, option (c) is the correct answer.
- Average of 10 two-digit positive integers = Z
- Average increases to Z+2.7 when one number AB is taken as BA
To find: |B - A|
Solution:
Let's assume that the sum of original 10 two-digit positive integers is S.
So, we can say that:
- Average of 10 two-digit positive integers = S/10 = Z
- Sum of 10 two-digit positive integers = S
When we interchange the digits of one number AB and make it BA, the sum of the 10 two-digit positive integers will increase by (BA - AB) = 9(B - A).
So, the sum of the 10 two-digit positive integers after this interchange will be (S + 9(B - A)).
Now, we know that:
- Average of 10 two-digit positive integers after the interchange = (S + 9(B - A))/10 = Z + 2.7
Substituting the value of Z from the first equation, we get:
(S + 9(B - A))/10 = (S/10) + 2.7
Simplifying this equation, we get:
9(B - A) = 27
B - A = 3
Therefore, the value of |B - A| is 3, which is option (c).
Hence, option (c) is the correct answer.
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