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

Question

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 p − q p + q ​ = 5 19 ​ , then p − q is equal to

TestHub · Accepted Answer

Let A ( a − d , a , a + d ) a = 12 p = 12 ( 144 − d 2 ) q = 12 ( 144 − D 2 ) p − q p + q ​ = 5 19 ​ ​ B ( b − D , b , b + D ) b = 12 ​ ​ q p ​ = 14 24 ​ = 7 12 ​ 144 − ( d 2 + 6 d + 9 ) 144 − d 2 ​ = 7 12 ​ 1008 − 7 d 2 = − 12 d 2 − 72 d + 1620 5 d 2 + 72 d − 612 = 0 d = 6 D = 9 p − q = 12 ( D 2 − d 3 ) = 12 ( 81 − 36 ) = 12 ( 45 ) = 540 option ( 4 ) ​

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