The sum of each of two sets of three terms in A.P is 15. The common difference of the first set is greater than that of the second by 1 and the ratio of the products of the terms in the first set and  that of the second set is 7:8 .the ratio of the smallest terms in two sets of terms is

Let the first set of number be a−d,a,a+d Then a−d+a+a+d=15⇒a=5  The  second set of numbers will be b−(d−1),b,b+(d−1) , again,b−(d−1)+b+b+(d−1)=15⇒b=5 Hence, the sets of numbers are 5−d,5,5+d  And6−d,5,4+d .Further , from the given  condition(5−d)5(5+d)(6−d)5(4+d)=78⇒25−d224+2d−d2=18 ⇒d2+14d−32=0⇒d=2,−16 ∴  the two sets are 3, 5, 7 and 4, 5, 6 or 21,5,–11 and 22,5,–12∴  ratio of their smallest term is 34  or −11−12  i. e 34  or 1112