Two arithmetic progressions have the same numbers. The ratio of the last term of the first progression to first term of the second progression is equal to the ratio of the last term of the second progression to the first term of the first progression and is equal to 4, the ratio of the sum of the  terms of the first progression to the sum of the  terms of the second progression is equal to 2   The ratio of their common difference is   a) 12 b) 24 c) 26 d) 9

Question ID - 51131 | Toppr Answer Two arithmetic progressions have the same numbers. The ratio of the last term of the first progression to first term of the second progression is equal to the ratio of the last term of the second progression to the first term of the first progression and is equal to 4, the ratio of the sum of the  terms of the first progression to the sum of the  terms of the second progression is equal to 2   The ratio of their common difference is   a) 12 b) 24 c) 26 d) 9

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(c)

Let the first term  and common difference  of the first A.P. and the first6 term  and commo0n difference  of the second A.P. and let the number of terms be . Then,

(1)

(2)

From (1) and (2), we get

(3)

(4)

(5)

gives

(6)

gives

(7)

Further,   gives

Or

Putting  in (3) and solving it with (4), we get

Then, the ratio of their  terms is