There are two sets A and B each of which consists of three numbers in A.P.whose sum is 15 and where D and d are the common differences such that `D-d=1. If p/q=7/8`, where p and q are the product of the numbers ,respectively, and ` d gt 0` in the two sets .
The sum of the product of the numbers in set B taken two at a time is

Options

A. 74
B. 64
C. 73
D. 81

Answer

A

Explanation

Let numbers in set A be a-D,a,a+D and those in set B be b-d,b,b+d. Now,
3a=3b=15
or a=b=5
Set A = {5-D,5,5+D}
set B = {5-d,5,5+d}
where D=d+1
Also,
`p/q=(5(25-D^(2)))/(5(25-d^(2)))=7/8`
`rArr25(8-7)=8(d+1)^(2)-7d^(2)`
`rArrd=-17,1` but `dgt0rArrd=1`
So, the numbers in set A are 3,5,7 and the nnumbers in set are 4,5,6.
Now, sum of product of numbers in set are 4,5,6.
Now, sum of product of numbers in set A taken two at a time is `3xx5+3xx7+5xx7=71`. The sum of product of numbers in set B taken two at a time is `4xx5+5xx6+6xx4=74`.
Also,
`p=3xx5xx7=105 and q=4xx5xx6=120`
`rArrq-p=15`