The bankers discount on a sum of money for 1$ \dfrac{1}{2} $ years is Rs. 558 and the true discount on the same sum for 2 years is Rs. 600. The rate percent is:

10%

13%

12%

15%

Explanation:

B.D. for $\dfrac{3}{2}$ years	= Rs. 558.
B.D. for 2 years	= Rs.$ \left(558 \times\dfrac{2}{3} \times 2\right) $
	= Rs. 744

T.D. for 2 years = Rs. 600.

$\therefore$ Sum =$ \dfrac{B.D. \times T.D.}{B.D. - T.D} $= Rs.$ \left(\dfrac{744 \times 600}{144} \right) $= Rs. 3100.

Thus, Rs. 744 is S.I. on Rs. 3100 for 2 years.

$\therefore$ Rate =$ \left(\dfrac{100 \times 744}{3100 \times 2} \right) $%= 12%