UGC NET Questions (Paper – 1)

From (a + b):(a − b) = 7:1, we have (a + b)/(a − b) = 7. This gives a + b = 7a − 7b. Rearranging, we get 8b = 6a, so a/b = 4/3. Therefore, the required ratio a:b is 4:3.

Option A:
Option A is correct because it is directly obtained by solving the equation derived from the ratio of sum to difference. Substituting a:b = 4:3 back into (a + b):(a − b) reproduces 7:1, verifying consistency with the original condition.

Option B:
Option B, 3:4, simply inverts the correct ratio and would imply that b is larger than a. Plugging a:b = 3:4 into (a + b):(a − b) yields a different ratio and does not give 7:1, so it fails the check.

Option C:
Option C, 5:3, might arise from mismanipulating terms or incorrectly handling coefficients when rearranging the equation. However, if a:b = 5:3, then (a + b):(a − b) simplifies to a ratio different from 7:1, so it is not acceptable.

Option D:
Option D, 7:3, uses the numerator from the given ratio as part of the answer but does not satisfy the algebraic relationship when substituted back. The resulting sum and difference ratio deviates from 7:1, demonstrating that 7:3 is incorrect.