The banker’s discount on a certain amount due 2 years

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The banker’s discount on a certain amount due 2 years hence is 11/10 of the true discount. What is the rate percent?

1. 1%
2. 5%
3. 10%
4. 12%

Correct Option: B

Let us assume that the True Discount = D
As per given question,
Banker’s discount = D x 11/10 = 11D/10
Time T = 2 Years
Rate of Interest R = ?
As we know the formula,

Banker's Discount =	Face value x Time x Rate of interest
	100

BD =	F x T x R
	100

Use the formula to get the face value, As we know that,

Face Value F =	Banker's Discount x True Discount
	Banker's Discount – True Discount

⇒ F =	BD x TD
	BD – TD

⇒ F =	D x 11D/10
	(11D/10) – D

⇒ F =	D x 11D/10
	(11D - 10D)/10

⇒ F =	D x 11D/10
	D/10

⇒ F =	D x 11
	1

⇒ F = 11D
As we know that from above formula,

BD =	F x T x R
	100

⇒ 11D/10 = 11D × 2 ×	R
	100

⇒ 1 = 1 × 2 x	R
	10

⇒ R =	10
	2

⇒ R = 5%