(A) Let the ten numbers be $x_1, x_2, ..., x_{10}$.The correct average is $A = \frac{\sum x_i}{10}$.Let the number with interchanged digits be $N = 10

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(A) Let the ten numbers be $x_1, x_2, ..., x_{10}$.The correct average is $A = \frac{\sum x_i}{10}$.Let the number with interchanged digits be $N = 10a + b$. The original number was $M = 10b + a$.The change in the sum of the numbers is $M - N = (10b + a) - (10a + b) = 9(b - a)$.Given that the average decreases by $1.8$,the total sum decreases by $1.8 \times 10 = 18$.Therefore,$9(b - a) = 18$.Dividing by $9$,we get $b - a = 2$.Thus,the difference between the digits of the number is $2$.

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$A$ student finds the average of ten $2$-digit numbers. While copying the numbers,by mistake,he writes one number with its digits interchanged. As a result,his answer is $1.8$ less than the correct answer. The difference between the digits of the number in which he made the mistake is:

A
$2$
B
$3$
C
$4$
D
$6$

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$A$ student finds the average of ten $2$-digit numbers. While copying the numbers,by mistake,he writes one number with its digits interchanged. As a result,his answer is $1.8$ less than the correct answer. The difference between the digits of the number in which he made the mistake is:

Similar Questions

$A$ cricketer,whose bowling average was $12.4$ runs/wicket,takes $5$ wickets for $22$ runs in a match,thereby decreasing his average by $0.4$. The number of wickets taken by him before this match was:

$A$ man travels by a car to his office at $60 \, km/h$ and returns home along the same route at $20 \, km/h$. Find the average speed of his whole journey (in $km/h$).

Out of nine persons,$8$ persons spent $Rs. 30$ each for their meals. The ninth person spent $Rs. 20$ more than the average expenditure of all the nine. What was the total money spent by all of them (in $Rs.$)?

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The average age of a cricket team reduces by $2$ when two senior players aged $32$ and $30$ are replaced by $2$ youngsters of equal age. What is the age of these youngsters?

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