In a set of prime and composite numbers,the n | vedclass

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

Question

(A) Let the average of prime numbers be $P$ and the average of composite numbers be $C$. Let the number of prime numbers be $x$,then the number of com

Vedclass · Accepted Answer

$\frac{7}{13}$

Vedclass · Answer

(A) Let the average of prime numbers be $P$ and the average of composite numbers be $C$. Let the number of prime numbers be $x$,then the number of composite numbers is $2x$.The average of all numbers is given by: $\frac{Px + C(2x)}{x + 2x} = 9 \Rightarrow \frac{Px + 2Cx}{3x} = 9 \Rightarrow P + 2C = 27$ (Equation $i$).If the counts are exchanged,the number of prime numbers becomes $2x$ and the number of composite numbers becomes $x$. The new average is $9 + 2 = 11$:$\frac{P(2x) + Cx}{2x + x} = 11 \Rightarrow \frac{2Px + Cx}{3x} = 11 \Rightarrow 2P + C = 33$ (Equation $ii$).Solving the system of equations:From $(i)$,$P = 27 - 2C$.Substitute into (ii): $2(27 - 2C) + C = 33 \Rightarrow 54 - 4C + C = 33 \Rightarrow 3C = 21 \Rightarrow C = 7$.Substitute $C = 7$ into $(i)$: $P + 2(7) = 27 \Rightarrow P + 14 = 27 \Rightarrow P = 13$.The ratio of the average of composite numbers to the average of prime numbers is $\frac{C}{P} = \frac{7}{13}$.

Similar Questions

$A, B, C$ and $D$ are four consecutive odd numbers and their average is $42$. What is the product of $B$ and $D$?

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

What is the average of the first $10$ even numbers?

The average age of $5$ sisters is $20 \, \text{years}$. If the age of the youngest sister is $4 \, \text{years}$,what was the average age of the group of sisters at the time of the birth of the youngest sister?

The average of $5$ quantities is $6$. The average of three of them is $8$. What is the average of the remaining two quantities?

Vedclass Test Series

Exam Paper Generator

Online Exam Module