# Aptitude - Banker's Discount - Discussion

### Discussion :: Banker's Discount - General Questions (Q.No.9)

9.

The banker's gain on a bill due 1 year hence at 12% per annum is Rs. 6. The true discount is:

 [A]. Rs. 72 [B]. Rs. 36 [C]. Rs. 54 [D]. Rs. 50

Explanation:

 T.D. = B.G. x 100 = Rs. 6 x 100 = Rs. 50. R x T 12 x 1

 Abc said: (Nov 14, 2011) Is it solved the same way as simple interest?

 Aneela said: (Jul 25, 2013) Can you say me how the discount is calculated. Is there any formulae for calculating it?

 Srira said: (Oct 6, 2014) Can you say me how the B.G is calculating?

 Radhika said: (Oct 6, 2014) Please explain this question and give another easy method.

 Sukumar Satyen said: (Apr 30, 2015) Following is detailed explanation: Banker's Gain (BG) is difference between Banker's Discount (BD) and True Discount (TD). => BG = BD - TD. => 6 = (F*R*T/100) - (PW*R*T/100). => 6 = (R*T/100)(F - PW). => 6 = (12/100)(F - PW). => 6*100/12 = F - PW. => F - PW = 50..........equation (1). We know, PW = F/{1+(T*R/100)} => F-[ F/{1+(T*R/100)}] = 50. => F-[ F/{1+(12/100)}] = 50. => F-[ F/{112/100 }] = 50. => F-[ F/{112/100 }] = 50. => F-[ 100 F/112 ] = 50. => (112 F-100 F)/112 = 50. => 12 F/112 = 50. => F = 50*112/12. Next, we need to calculate Present Worth (PW). => PW = F/{1+(T*R/100)}. => PW = (50*112/12)/{1 + (12/100)}. => PW = (50*112/12)/{112/100}. => PW = (50*112*100)/(112*12). => PW = 50*100/12. Present Worth (PW) can also be calculated from equation (1): => F-PW = 50. => PW = F-50. => PW = 50*112/12-50. => PW = (50*112-50*12)/12. => PW = 50*(112-12)/12. => PW = 50*100/12. NOW, we can calculate True Discount (TD), which is simple interest on Present Worth (PW). => TD = PW*R*T/100. => TD = (50*100/12)*(12/100). => TD = Rs. 50. Thanks.