In a set of prime and composite numbers, composite numbers are twice number of prime number and aver

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In a set of prime and composite numbers, the composite numbers are twice the number of prime number 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

$\frac{7}{13}$

$\frac{13}{7}$

$\frac{9}{11}$

$\frac{7}{11}$

Solution

Let the average of prime number be $P$ and average of composit number be $C.$ Again the number of prime number be $x$, then the number of composite number be $2 x$

$\frac{P x+2 C x}{3 x}=9 \Rightarrow P+2 C=27$

$\frac{2 P x+C x}{3 x}=11 \Rightarrow 2 P+C=33$

On adding eq. (i) and (ii)

we get $P+C=20$ and on Subtracting eq. (i) from (ii)

we get $P-C=6$

Therefore $P=13$ and $C=7 \Rightarrow$ thus $=\frac{C}{P}=\frac{7}{13}$

Standard 13

Quantitative Aptitude

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Solution

Similar Questions

$A , B , C , D\, \& \,E$ are five consecutive even numbers. Average of $A$ and $E$ is $46 .$ What is the largest number?

Out of seven given numbers, the average of the first four numbers is $4$ and that of the last four numbers is also $4 .$ If the average of all the seven numbers is $3,$ then fourth number is?

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