(D) Let the total number of students be $N$. The total height of all students is $T = aN$.The sum of heights of $10$ students is $10b$.The number of r

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

(D) Let the total number of students be $N$. The total height of all students is $T = aN$.The sum of heights of $10$ students is $10b$.The number of remaining students is $(N-10)$,and their total height is $(N-10)c$.The sum of the heights of the two groups equals the total height of the class:$10b + (N-10)c = aN$Expand the equation:$10b + Nc - 10c = aN$Rearrange to solve for $N$:$10b - 10c = aN - Nc$$10(b-c) = N(a-c)$Therefore,the total number of students is:$N = \frac{10(b-c)}{a-c}$

Competitive Quantitative Aptitude Average Average

Difficult

In a class,the average height of all students is $a \text{ cm}$. Among them,the average height of $10$ students is $b \text{ cm}$ and the average height of the remaining students is $c \text{ cm}$. Find the number of students in the class. (Here $a > c$ and $b > c$)

A
$\frac{a(b-c)}{a-c}$
B
$\frac{b-c}{a-c}$
C
$\frac{b-c}{10(a-c)}$
D
$\frac{10(b-c)}{a-c}$

Explore More

Browse All

Question Bank

All Subjects

Competitive Questions

Competitive

Quantitative Aptitude Questions

Chapter

Average

Subtopic

Average

Ashish has earned an average of $4200$ dollars for the first eleven months of the year. If he justifies his staying on in the $US$ on the basis of his ability to earn at least $5000$ dollars per month for the entire year,how much should he earn (in dollars) in the last month to achieve his required average for the whole year?

Medium

View Solution

Amitabh's average expenditure from $January$ to $June$ is $Rs. 4200$. He spends $Rs. 1200$ in $January$ and $Rs. 1500$ in $July$. What is the average expenditure for the months of $February$ to $July$ (in $Rs.$)?

Easy

View Solution

The average of runs scored by a cricketer in his $99$ innings is $99$. How many runs will he have to score in his $100^{\text{th}}$ innings so that his average of runs in $100$ innings may be $100$?

Medium

View Solution

The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

Medium

View Solution

$A$ student was asked to find the arithmetic mean of the numbers $3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14$ and $x$. He found the mean to be $12$. What should be the number in place of $x$?

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

In a class,the average height of all students is $a \text{ cm}$. Among them,the average height of $10$ students is $b \text{ cm}$ and the average height of the remaining students is $c \text{ cm}$. Find the number of students in the class. (Here $a > c$ and $b > c$)

Similar Questions

Amitabh's average expenditure from $January$ to $June$ is $Rs. 4200$. He spends $Rs. 1200$ in $January$ and $Rs. 1500$ in $July$. What is the average expenditure for the months of $February$ to $July$ (in $Rs.$)?

The average of runs scored by a cricketer in his $99$ innings is $99$. How many runs will he have to score in his $100^{\text{th}}$ innings so that his average of runs in $100$ innings may be $100$?

The mean of $11$ numbers is $35$. If the mean of the first $6$ numbers is $32$ and that of the last $6$ numbers is $37$, then find the sixth number.

$A$ student was asked to find the arithmetic mean of the numbers $3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14$ and $x$. He found the mean to be $12$. What should be the number in place of $x$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module