The true discount on a certain sum due 6 months hence at

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The true discount on a certain sum due 6 months hence at 15 % is Rs. 240. What is the banker’s discount on the same sum for the same time at the same rate?

1. Rs. 248
2. Rs. 278
3. Rs. 228
4. Rs. 258

Correct Option: D

Given in the question,
True Discount = 240
Rate of interest = 15%
Time = 6 months = 1/2 year
As we know the formula ,

True Discount = Banker's Gain ×	100
	Time in years x Rate of Interest

⇒ 240 = Banker's Gain ×	100
	(1/2 × 15)

⇒ 240 = Banker's Gain ×	100 x 2
	(1 × 15)

⇒ 24 = Banker's Gain ×	10 x 2
	(1 × 15)

⇒ 24 = Banker's Gain ×	2 x 2
	(1 × 3 )

⇒ 6 = Banker's Gain ×	1
	3

⇒ Banker's Gain = Rs. 6 x 3
⇒ Banker's Gain = Rs. 18
Apply the formula, As we know that ,
Banker's Gain = Banker's Discount − True Discount
⇒ 18 = Banker's Discount − 240
⇒ Banker's Discount = Rs. 258