Question

In a set of prime and composite numbers, the composite numbers are twice the number of prime numbers and the average of all the numbers of the set is 9. If the number of prime numbers and composite numbers are exchanged, then the average of the set of numbers is increased by 2. If during the exchange of the numbers the average of the prime numbers and composite numbers individually remained constant, then the ratio of the average of composite numbers to the average of prime numbers (initially) was

• A. $\frac{7}{13}$
• B. $\frac{13}{7}$
• C. $\frac{9}{11}$
• D. None of these

Answer 1

The correct option is A $\frac{7}{13}$

Let the average of prime numbers be P and average of composite numbers be C.
Again let the number of prime numbers be x, then the number of composite numbers be 2x.
Then $\frac{Px+2Cx}{3x}=9\Rightarrow P+2C=27$ ...(1)
and $\frac{2Px+Cx}{3x}=11$
$\Rightarrow 2P+C=33$ ...(2)
On adding eq. (1) and (2)
we get P + C = 20
and on subtracting eq. (1) and (2)
we get P - C = 6
Therefore P = 13 and C = 7
Thus $\frac{C}{P}=\frac{7}{13}$