There are two sets `M_1` and `M_2` each of which consists of three numbers in arithmetic sequence whose sum is 15. Let `d_1` and `d_2` be the common differences such that `d_1=1+d_2` and `8p_1=7p_2` where `p_1` and `p_2` are the product of the numbers respectively in `M_1` and `M_2`. If `d_2 gt 0` then find the value of `(p_2-p_1)/(d_1+d_2)`

Options

A. 20
B. 30
C. 15
D. 25

Answer

C

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`