(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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(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 $2$.

Competitive Quantitative Aptitude Average Average

Easy

$A$ 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
$6$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Average

Subtopic

Average

The average age of a family of $6$ members is $22 \text{ years}$. If the age of the youngest member is $7 \text{ years}$,then what was the average age of the family at the birth of the youngest member?

Medium

View Solution

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children,respectively. The average marks obtained by the children of group $A$ is $75$ and that of all the children is $76$. Then,the average marks of the children of group $B$ is?

Medium

View Solution

The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is

Medium

View Solution

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?

Medium

View Solution

After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

$A$ 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

The average age of a family of $6$ members is $22 \text{ years}$. If the age of the youngest member is $7 \text{ years}$,then what was the average age of the family at the birth of the youngest member?

$16$ children are to be divided into two groups $A$ and $B$ of $10$ and $6$ children,respectively. The average marks obtained by the children of group $A$ is $75$ and that of all the children is $76$. Then,the average marks of the children of group $B$ is?

The arithmetic mean of the scores of a group of students in a test was $52$. The brightest $20\%$ of them secured a mean score of $80$ and the dullest $25\%$ a mean score of $31$. The mean score of the remaining $55\%$ is

If the average of the ages of Rakesh and Mohan is $15$,the average of the ages of Mohan and Ramesh is $12$,and the average of the ages of Rakesh and Ramesh is $13$,then what is the age of Mohan?

After replacing an old member with a new member,it was found that the average age of five members of a club is the same as it was $3 \, \text{years}$ ago. What is the difference between the ages of the replaced member and the new member (in $\text{years}$)?

Vedclass Test Series

Exam Paper Generator

Online Exam Module