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Question

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


A

34 or 1112

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B

23 or 12

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C

23 or 34

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D

None

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Solution

The correct option is A

34 or 1112


Let the first set of number be ad,a,a+d.
Then ad+a+a+d=15a=5
The second set of numbers will be
b(d1),b,b+(d1).Again,b(d1)+b+b+(d1)=15b=5
Hence the sets of numbers are
5d,5,5+d and 6d,5,4+d.
Further, from the given condition
(5d)5(5+d)(6d)5(4+d)=7825d224+2dd2=18
d2+14d32=0d=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 1112i.e.34 or 1112


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