Consider two sets A and B , each containing three numbers in A.P.… - Vidyadip

MCQ

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 $D=d+3, d>0$. If $\frac{p+q}{p-q}=\frac{19}{5}$, then $p-q$ is equal to

A
600
B
450
C
630
✓
540

✓

Answer

Correct option: D.

540

(D) 540
$\text {Let}$ $A(a-d, a, a+d) B(b-D, b, b+D) $
$\quad a=12 \quad\quad\quad\quad\quad\quad b=12 $
$p=12\left(144-d^2\right)$
$q=12\left(144-D^2\right) $
$\frac{p+q}{p-q}=\frac{19}{5}$
$\frac{p}{q}=\frac{24}{14}=\frac{12}{7} $
$\frac{144-d^2}{144-\left(d^2+6 d+9\right)}=\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\right) $
$=12(81-36) $
$=12(45) $
$=540$

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