CAT / #Quantitative Ability

October 27, 2017 @ 11:27 AM

Tricky Questions on Banker's Discount

CAT QA

Theoretical Concept:

Suppose a merchant Ram buys goods worth. say Rs.1,00,000 from another merchant Shyam at a credit of say 10 months. Then, Shyam prepares a bill, called the bill of exchange. Ram signs this bill and allows Shyam to withdraw the amount from his bank account after exactly 10 months.

The date exactly after 10 months is called nominally due date. Three days {known as grace days) are added to it get a date, known as legally due date.

Suppose Shyam wants to have the money before the legally due date. Then he can have the money from the banker or a broker. Who deducts S.I. {Simple Interest) on the face value (i.e., Rs.1,00,000in this case) for the period from the date on which the bill was discounted (i.e., paid by the banker) and the legally due date. This amount is known as Banker's Discount {B.D.).

Thus, B.D.is the S.I. on the face value for the period from the date on which the bill was discounted and the legally due date.

Banker's Gain {B.G.) = {B.0.) - (T.D.) for the unexpired time.

Note: When the date of the bill is not given, grace days are not to be added.

Important Formulas:

i)  B.D.= S.I. on bill for unexpired time.

ii) B.G.= {B.D.).(T.D.) = S.I. on T.D.= (T.D.)*P.V.

iii) T.D.=  P.W. x B.G.  

iv) B.D.= [(Amount x Rate x Time)/100]

v) T.D.= ({Amount x Rate x Time)/ 100 + (Rate x Time)] vi) Amount = ((B.D.x T.D.)/ B.D.*T.D]

vii) T.D.= ((B.G. x 100)/ (Rate x Time)]

Solved Illustrations:

Question 1)

The banker's discount on a bill due 4 months hence at 15%is Rs. 420.The true discount is:

A.

Rs.400

B. Rs.360

c.

Rs.480

D. Rs.320

Answer: Option A

Solution:

T.D.= B.D. x 100/ 100 + (R x T)

= Rs. [420 x 100/100 + (15*1/3))

= Rs.420 x 100/ 105 = Rs.400

Question 2)

The banker's discount on Rs.1600 at 15% per annum is the same as a true discount on Rs. 1680 for the same time and at the same rate. The time is:

A.

3 months

B.

4 months

c.

6 months

D.

8 months

Answer: Option B

Solution:

S.I. on Rs.1600 = T.D. on Rs.1680.

Rs.1600 is the P.W. of Rs.1680, i.e., Rs.80 is on Rs.1600 at 15%. Time = {100 x 80/ 1600 x 15} Years = 1/3 years = 4 months

Question3)

The banker's discount on a sum of money for 11/2 years (one and half years) is Rs.558 and the true discount on the same sum for 2 years is Rs. 600.The rate percent is:

A.

10%

B.

 13%

c.

12%

D.

 15%

Answer: Option C

Solution:

B.D. for 3/2 years = Rs.558.

B.D. for 2 years = Rs.558.2/3.2 = Rs.744

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

Therefore, sum = B.D.*T.D./B.D.- T.D.=Rs. [744 *600/144) = Rs.3100

Thus, Rs.744 is 5.1. on Rs.3100 for 2 years.

Therefore, Rate = [(100 *744)/ (3100 x 2)) % = 12%

Question 4)

The banker's gain on a certain sum due 11/2 year hence is 3/2!5 of the banker's discount. The rate percent is:

A.

5 1⁄2 %

B.

9 1⁄11 %

c.

8 1⁄8 %

D.

6 1⁄6 %

Answer: Option B

Solution:

let, B.D = Re.1.

Then. B.G.= Re.3/25

T.D.= {B.D.- B.G.) = Re. {1- 3/25) = Re.22/25 Sum = [1x {22/25)/ 1-{22/25)) = Re.22/3

S.I. on Rs.22/3 for 11/2 years is Re.1

Rate = [100 x 1/ {22/3*3/2)) % = 100/11= 9 1/11%

Question 5)

The banker's discount on a certain sum due 2 years hence is 11/10 of the true discount. The rate percent is:

A.

11%

B

10%

c.

5%

D.

5.5%

Answer: Option C

Solution:

let T.O. be Re.1.

Then,8.0. = Rs.11/10 = Rs.1/10

Sum = Rs. ((1.10 x 1)/ {1.10 - 1)) = 110/10 = Rs.11

S.I. on Rs.11 for 2 years is Rs.1.10

Rate = ((100"1.10}/ (11*2)) % = 5%

Attempt CAT Mock Test Now

Read Complete Module on Quantitative Ability

Stay informed, Stay ahead & Stay inspired with MBA Rendezvous 

Crucial Dates, You Should not Miss

TAPMI, Manipal
Admission Application closes on January 16, 2018 for 2018-20
BIMTECH, Greater Noida
Admissions open for PGDM Programmes at BIMTECH. Apply Now !
Lal Bahadur Shastri Institute of Management
Admissions are Open at LBSIM, Delhi. Apply Now !
FORE School of Management
Apply for PGDM & PGDM-IB Programmes. Application Deadline is December 22, 2017.
Goa Institute of Management
PGDM Admissions Open at GIM. Apply Before January 5, 2018
NIRMA
Last Date to Apply for MBA (Full Time) Programme at NIRMA is January 09, 2018
XAT 2018
Application Last Date 30th November 2017
IMI New Delhi
Application closes 4th December 2017
XIM Bhubaneshwar
Last Date 8th December 2017
SIBM Bengaluru
Apply for SNAP 2017 to be held on Dec 17 and apply for SIBM-Bengaluru through the SNAP Form
Institute of Rural Management Anand
IRMASAT will be conducted on February 4,2018, Apply Before December 31,2017
IBSAT 2017
Last date for IBSAT registration is December 12 , 2017
SSBF
Last date to register for SNAP is 24th November, 2017. Last date for SSBF is 2nd January 2018
SIBM Hyderabad
Apply for SNAP 2017 to be held on Dec 17 and apply for SIBM-Hyderabad through the SNAP Form
K J Somaiya Institute of Management Studies & Research, Mumbai
Last date for Application is 31st Jan, 2018
SDMIMD Mysore
Application for PGDM 2018-20 at SDMIMD is open till February 28, 2018
Institute of Management Technology
Application closes on November 24, 2017
MDI Murshidabad
Application for PGPM 2018-20 at MDI Murshidabad is open till November 24, 2017

Admission Open Now

Following Colleges are accepting applications.

INTERNATIONAL MANAGEMENT INSTITUTE

Admissions open for 2018-20

PGDM, PGDM (HRM), PGDM(B & FS), Executive PGDM

Apply Online