Consider two sets $A$ and $B$, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that…

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Consider two sets $A$ and $B$, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively and the sum and the product of the elements of B be 36 and q respectively. Let d and D be the common differences of AP's in A and B respectively such that $D=d+3, d \gt 0$. If $\frac{p+q}{p-q}=\frac{19}{5}$, then $p-q$ is equal to

Aicharya · Accepted Answer

$\begin{array}{lc}	ext { Let } A(a-d, a, a+d) & B(b-D, b, b+D) \ \quad a=12 & b=12 \ p=12\left(144-d^2ight) & \ q=12\left(144-D^2ight) & \ \frac{p+q}{p-q}=\frac{19}{5} & \end{array}$ $\begin{aligned} & \frac{p}{q}=\frac{24}{14}=\frac{12}{7} \ & \frac{144-d^2}{144-\left(d^2+6 d+9ight)}=\frac{12}{7} \ & 1008-7 d^2=-12 d^2-72 d+1620 \ & 5 d^2+72 d-612=0 \ & d=6 \ & D=9 \ & p-q=12\left(D^2-d^3ight) \ & =12(81-36) \ & =12(45) \ & =540 \ & 	ext { option }(4)\end{aligned}$ *

Consider two sets $A$ and $B$, each containing three numbers in A.P. Let the sum and the product of the…

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