Babita was asked

Question

Babita was to calculate the arithmetic mean of ten positive two digit integers. By miatake, she interchanged the two digits, say t & u, in one of these ten integers. As a result, her answer for arithmetic mean was 1.8 more than what it should have been. Then u-t equals

(A) 1
(B) 2
(C) 3
(D) 4

(A) 1
(B) 2
(C) 3
(D) 4

archit1996 · Answer

The answer is B. 
Lets say the 9 integers be Y and the changed integer be X. 
So X= 10t+u and X' = 10u+t is the number that was mistakingly calculated. 
Now, mean = (X+Y)/10 
mean' = (X'+Y)/10
Subtracting, 
mean' - mean = (X' - X)/10
1.8= (X'-X)/10
18=(X'-X) 
18= (10u+t)-(10t+u)
18= 9u-9t
18= 9(u-t) 
2=(u-t)

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MathRevolution · Answer

Hi Harshit401,

Let the interchanged integer 10t + u.
It is changed to 10u + t.

( 10u + t ) - ( 10t + u ) = 10 ( u - t ) + ( t - u ) = 9 ( u - t ) = 18
Then u - t = 2
The answer is B.

Happy Studying!
Math Revolution

ManifestDreamMBA · Answer

If Avg increased by 1.8, that means the sum of all numbers increased by 18.
We know that for a 2digit number 10a-b, if we interchange the values, the difference is a multiple of 9*difference b/w the digits = 9(a-b) = 18.
This leads to a-b =2, which is u-t in the question

Babita was asked

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