The banker's gain on a certain sum due 21/2 years hence

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The banker's gain on a certain sum due 2¹/₂ years hence is (3/23)
of the banker's discount. The rate per cent is ?

1. 5%
2. 6%
3. 2¹⁴/₂₃%
4. 6²3%

Correct Option: B

Let B.D. be Re. 1. Then B.G. = Re. (3/23)
∴ T.D.= Re. (1 - 3/23) = Re. (20/23)
Sum = Rs. [(1 x 20/23 / (1 - 20/23)] = Rs. 20/3
∴ S.I. on Rs. 20/3 for 2¹/₂ years is Re. 1
∴ Rate = (100 x 1 / 20/3 x 5/2)% = 6%