When
chiken prices rise 40%, the quantity of KFC fried chicken
supplied
rises by 20%. Calculate the price
elasticity
of supply.
a.
0.25
b.
0.50
c.
0.75
d.
0.85
Ans
- a
Solution
:
Price
Elasticity of Supply = (% change in quantity supplied) / (%
change
in price)
=
20/40 = 0.5
When
the price of a commodity falls from Rs. 60 per unit to
Rs.
48 per unit, the quantity supplied falls by
20%.
Calculate the price elasticity of supply.
a.
1
b.
1.5
c.
2
d.
2.5
Ans
– a
495
Solution
:
Price
Elasticity of Supply = (% change in quantity supplied) / (%
change
in price)
=
20/((60-48)*100/60)
=
20/(12*100/60)
=
20/20
= 1
21
bricks have a mean mass of 24.2 kg, and 29 similar bricks
have
a mass of 23.6 kg. Determine the
mean
mass of the 50 bricks.
a.
18.35 kg
b.
20.35 kg
c.
23.85 kg
d.
32.85 kg
Ans
- c
Solution
:
Mean
value = ((21 x 24.2) + 29 x 23.6 )) / (21+29)
=
1192.6 / 50
=
23.85 kg
.............................................
Net
income available to stockholders is ₹150 and total assets
are
₹2,100 then return on total assets
would
be ......
a.
0.07%
b.
7.14%
c.
0.05 times
d.
7.15 times
Ans
- b
Solution
Return
on Assets Ratio=Net Income/Average Total Assets*100
=150/2100*100
=0.0714
=7.14
.............................................
Given,
Recoveries
of loan and advance - Rs. 3000 Crores
Misc
capital receipt - Rs. 600 Crores
Market
loAns - Rs. 600 Crores
Short
term borrowings - Rs. 1200 Crores
External
assistance (Net) - Rs. 500 Crores
State
provident fund - Rs. 600 Crores
Other
receipts (Net) - Rs. 1200 Crores
Securities
issued against small savings - Rs. 600 Crores
Recoveries
of short term loans and advances from states and
loans
to govt servants - Rs. 1000 Crores
Total
Non Tax Revenue - Rs. 5000 Crores
Net
Tax Revenue - Rs. 2000 Crores
Draw
down cash balance - Rs. 4000 Crores
Calculate
Debt Receipt ...
a.
Rs 2500 Crores
b.
Rs 3700 Crores
c.
Rs 4700 Crores
d.
Rs 5400 Crores
Ans
- c
.............................................
Calculate
Non Debt Receipt ...
a.
Rs 2500 Crores
b.
Rs 3700 Crores
c.
Rs 4700 Crores
d.
Rs 5400 Crores
Ans
- a
.............................................
Calculate
Capital Receipt ...
a.
Rs 4700 Crores
b.
Rs 5400 Crores
c.
Rs 6200 Crores
d.
Rs 7200 Crores
Ans
- c
.............................................
Solution
:
1.
Debt Receipt = Market Loans + Short Term Borrowings +
External
assistance(NET) + Securities issued
against
Small savings + State provident fund + other
Receipts(Net)
=
600 + 1200 + 500 + 600 + 600 + 1200
=
3700 Crores
2.
Non Debt Receipt = Recoveries of loan & advances (deduct
recoveries
of short term loans & advance
from
state and loans to govt sarvants) + MISC Capital receipts
=
(3000-1000)+500
=
2500 Crores
3.
Capital Receipt = Non Debt Receipt + Debt Receipt
=
3700 + 2500
=
6200 Crores
Given,
Currency
with public - Rs. 120000 Crores
Demand
deposit with banking system - Rs. 200000 Crores
Time
deposits with banking system - Rs. 250000 Crores
Other
deposit with RBI - Rs. 300000 Crores
Savings
deposit of post office savings banks - Rs. 100000
Crores
All
deposit with post office savings bank excluding NSCs - Rs.
50000
Crores
1.
Calculate M1.
a.
Rs. 570000 Crores
b.
Rs. 620000 Crores
c.
Rs. 670000 Crores
d.
Rs. 720000 Crores
Ans
- b
.............................................
2.
Calculate M2.
a.
Rs. 570000 Crores
b.
Rs. 620000 Crores
c.
Rs. 670000 Crores
d.
Rs. 720000 Crores
Ans
- d
.............................................
3.
Calculate broad money M3.
a.
Rs. 570000 Crores
b.
Rs. 620000 Crores
c.
Rs. 670000 Crores
d.
Rs. 870000 Crores
Ans
- d
.............................................
Solution
:
1.
M1 = currency with public + demand deposit with the
banking
system + other deposits with RBI
M1
= 120000+200000+300000
M1
= 620000
485
2.
M2 = M1+Savings deposit of post office savings banks
So,
M2
= 620000+100000
M2
= 720000 Crores
3.
M3 = M1+Time deposit with banking system
So,
M3
= 620000+250000
M3
= 870000 Crores
Given
1. Consumptions
- Rs. 50000
2.
Gross investment - Rs. 40000
3.
Govt spending - Rs. 10000
4.
Export - Rs. 90000
5.
Import - Rs. 60000
6.
Indirect Taxes - Rs. 10000
7.
Subsidies(on production and import) - RS. 5000
8.
Compensation of employee - Rs. 500
9.
Property Income - Rs. 500
7,8,9
- Net receivable from aboard
10.Total
capital gains from overseas investment - Rs. 15000
11.Income
earned by foreign national domestically - Rs. 5000
1.
Calculate GDP
a.
Rs. 125000
b.
Rs. 130000
c.
Rs. 135000
d.
Rs. 140000
Ans
- b
.............................................
2.
Calculate GDP at cost factor
a.
Rs. 125000
b.
Rs. 130000
c.
Rs. 135000
d.
Rs. 140000
Ans
- c
.............................................
3.
Calculate GNP
a.
Rs. 110000
b.
Rs. 120000
c.
Rs. 130000
d.
Rs. 140000
Ans
- d
.............................................
479
Solution
:
1.
GDP = Consumption + Gross investment + Government
spending
+ (Exports - Imports)
GDP
= C+I+G+(X-M)
=
50000+40000+10000+(90000-60000)
=
130000
2.
GDP at factor rate
=
GDP-(Indirect taxes-subsidies)
=
130000-(10000-5000)
=
135000
3.
GNP=GDP+NR(total capital gains from Overseas
investment-income
earned by foreign national
domestically)
=
130000 + (15000-5000)
=
140000
.............................................
Savings
deposit of post office savings banks - Rs. 60000 Crores
All
deposit with post office savings bank excluding NSCs - Rs.
50000
Crores
Calculate
M4.
a.
Rs. 750000 Crores
b.
Rs. 800000 Crores
c.
Rs. 810000 Crores
d.
Rs. 870000 Crores
Ans
- b
Solution
:
M4
= M3+All deposit with post office savings bank excluding
NSCs
M3
= M1+Time deposit with banking system
M1
= currency with public + demand deposit with the banking
system
+ other deposits with RBI
M1
= 90000+180000+260000
M1
= 530000
So,
M3
= M1+Time deposit with banking system
M3
= 530000+220000
M3
= 750000 Crores
So,
M4
= M3+All deposit with post office savings bank excluding
NSCs
M4
= 750000+50000
M4
= 800000 Crores
Calculate
the present value of 6 year bond with 9 per cent
coupon
rate with FV Rs. 1000/-. Current
interest
rate is 12 per cent.
a.
Rs.843.83
b.
Rs.1025.57
c.
Rs.876.66
d.
Rs.768.68
Ans
- c
Solution
FV
= 1000
Coupon
Rate (CR) = 0.9%
t =
6 year
R
(YTM) = 0.12
Annual
interest rate payable=1000*9%=90
Principal
repayment at the end of 6 year = Rs. 1000
=90
(PVIFA, 12%,6 years)+1000(PVIF,12%, 6 Years)
PVIFA=
((1+r)^t -1)/ r+ PVIF=1/(1+R)^t
=90(1.12^6-1/0.12*(1.12)^6+1000(1/1.12^6)
=90*1.97382-1/0.12*1.1.97382+1000(1/1.97382)
=90*0.97382/0.12*1.97382+1000*0.0.50663
=90*0.97382/0.23685+506.63
=90*4.11154+506.63
=370.03+506.63
=876.66
Mr
x is to receive Rs. 10000, as interest on bonds by end of
each
year for 5 years @ 5% roi. Calculate the
present
value of the amount he is to receive.
a.
43925
b.
43295
c.
49325
d.
49235
Ans
- b
Explanation
:
Here,
P =
10000
R =
5% p.a.
T =
5 Y
PV
= P / R * [(1+R)^T - 1]/(1+R)^T
PV
to be received, if the amount invested at end of each year:
So,
FV
= (100000÷0.05) * {(1+0.05)^5 – 1} ÷ (1+0.05)^5
=
43295
A
company has net worth of Rs. 15 lac, term liabilities are Rs.
10
lac. Fixed Assets worth Rs. 16 lac and
current
assets are Rs. 25 lac. There is no intangible assets or
the
non current assets. Calculate it's net
working
capital.
a.
6 lac
b.
7 lac
c.
8 lac
d.
9 lac
Ans
- d
Total
Assets = Total liabilities
Total
Assets = Fixed Assets + current assets
=
16 + 25
=
41
So
total liabilites must be 41 lac
Now
out of 41 lac, the long term liability is 25 lac (15 + 10)
Hence
CL = 41 - 25 = 16 lac
Now
we have CA = 25 lac and CL = 16 lac
NWC
= 25 - 16
= 9
lac
.............................................
Calculate
Standard Error from the given data : X = 10,
20,30,40,50
a.
6.1071
b.
6.0711
c.
7.1071
d.
7.0711
Ans
- d
Explanation
:
Total
Inputs (N) = (10,20,30,40,50)
Total
Inputs (N) =5
First
find Mean:
Mean
(xm) = (x1+x2+x3...xn)/N
Mean
(xm) = 150/5
Mean
(xm) = 30
Then
find SD:
SD
= √(1/(N-1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))
= √(1/(5-1)((10-30)2+(20-30)2+(30-30)2+(40-30)2+(50-30)2))
= √(1/4((-20)2+(-10)2+(0)2+(10)2+(20)2))
= √(1/4((400)+(100)+(0)+(100)+(400)))
= √(250)
=
15.811
Then
Find Standard Error:
Standard
Error=SD / √(N)
=
15.8114/√(5)
=
15.8114/2.2361
=
7.0711
A
sack contains 4 black balls 5 red balls. What is probability to
draw
1 black ball and 2 red balls in one
draw
?
a.
12/21
b.
9/20
c.
10/21
d.
11/20
Ans
– c
Solution
:
Out
of 9, 3 (1 black & 2 red. are expected to be drawn)
Hence
sample space
n(S)
= 9c3
=
9!/(6!×3!)
=
362880/4320
=
84
Now
out of 4 black ball 1 is expected to be drawn hence
nb.
= 4c1
= 4
Same
way out of 5 red balls 2 are expected be drawn hence
n(R)
= 5c2
=
5!/(3!×2!)
=
120/12
=
10
Then
P(B U R) = n(B)×n(R)/n(S)
i.e
4×10/84 = 10/21
........................................................
Quantity
supplied of a product at Rs. 8 per unit is 200 Units. If
the
price elasticity of supply is 1.5, what
will
be the quantity supplied at Rs. 10 per unit?
a.
150
b.
175
c.
250
d.
275
Ans
- d
Solution
:
Price
Elasticity of Supply = (% change in quantity supplied. / (%
change
in price)
1.5
= ((x-200)*100/200)/((10-8)*100/8)
1.5
= ((x-200)/2)/(200/8)
1.5
= ((x-200)/2)/25
1.5
= (x-200)/50
75
= x-200
x =
75+200
x =
275
X
opened a recurring account with a bank to deposit Rs. 16000
by
the end of each year @ 10% roi. How
much
he would get at the end of 3rd year?
a.
52960
b.
52690
c.
52069
d.
52096
Ans
- a
Explanation
:
Here,
P =
16000
R =
10% p.a.
T =
3 yrs
FV
= P / R * [(1+R)^T - 1]
FV
= 16000 * (1.13 – 1) ÷ 0.1
=
52960
.............................................
Find
Correlation coefficient for X and Y values given below :
X=
(1,2,3,4,5)
Y=
{11,22,34,43,56}
a.
0.8899
b.
0.9989
c.
1.0899
d.
1.0989
Ans - b
Explanation
:
Step
1: Find Mean for X and Y
X=15/5=3
Y=166/5=33.2
Step
2: Calculate Standard Deviation for Y inputs:
σx=
359
√(1/(N-1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))
=√(1/(5-1)((11-33.2)2+(22-33.2)2+(34-33.2)2+(43-33.2)2+(56-
33.2)2))
=√(1/4((-22.2)2+(-11.2)2+(0.8)2+(9.8)2+(22.8)2))
=√(1/4((492.84)+(125.44)+(0.64)+(96.04)+(519.84)))
=√(308.7)
=17.5699
Step
3: Standard Deviation for X Inputs:
σx=
√(1/(N-1)*((x1-xm)2+(x2-xm)2+..+(xn-xm)2))
=√(1/(5-1)((1-3)2+(2-3)2+(3-3)2+(4-3)2+(5-3)2))
=√(1/4((-2)2+(-1)2+(0)2+(1)2+(2)2))
=√(1/4((4)+(1)+(0)+(1)+(4)))
=√(2.5)
=1.5811
Σ((X
- μx) (Y - μy))
=(1-3)(11-33.2)+(2-3)(22-33.2)+(3-3)(34-33.2)+(4-3)(43-
33.2)+(5-3)(56-33.2)
=(-2*-22.2)
+ (-1*-11.2) + (0* 0.8) + (1 *9.8) + (2* 22.8)
=44.4
+ 11.2 + 0 + 9.8 + 45.6
=111
Correlation
Coefficient = 111/((5-1)*1.5811*17.5699)
Correlation
Coefficient (r) = 0.9989
Hence
the correlation coefficient between the two given data
set
is 0.9989
Albert
purchased 8%, 3 years bond of Rs. 10 lac, with annual
interest
payment and face value payable on
maturity.
The YTM is assumed@ 6%. Calculate the duration
and
modified duration.
a.
2.36
b.
2.79
c.
2.63
333
d.
2.97
Ans
- c
Explanation
:
Bond’s
Duration = ΣPV×T ÷ ΣP
ΣP
= 1053421
Now,
a = 0.943396 and a^t = 0.839619
So,
ΣPV×T = 80000 × 16.666 × (0.160381÷0.056604 –
2.518857)
+ 2518857
=
419370.767 + 25188579
=
2938227.77
So,
Duration of the Bond
=
2938227.77 / 1053421
=
2.79 years
&
Modified Duration
=
Mckauley Duration ÷ (1 + R)
=
2.79 ÷ 1.06
=
2.63
Mr.
Raj is to invest Rs. 100000 by end of each year for 5 years
@
5% roi. How much amount he will
receive?
a.
556253
b.
553562
c.
552563
d.
555263
Ans
- c
Explanation
:
Here,
P =
1000000
R =
5% p.a.
T =
5 Y
FV
= P / R * [(1+R)^T - 1]
FV,
if invested at end of each year, is:
So,
FV
= (100000÷0.05) * {{1+0.05}^5 – 1}
=
552563
An
urn contains 10 black balls and 5 white balls. 2 balls are
drawn
from the urn one after other without
replacement.
What is the probability that both drawn are
black
?
a.
2/7
b.
3/7
c.
4/7
d.
6/7
Ans
- b
Solution
:
Let
E and F denote respective events that first and second ball
drawn
are black.
We
have to find here P(E n F ) and P(E/F)
Now
P(E) = P(Black in first drawn) = 10/15
Also
given that the first ball is drawn i.e events E has occurred.
Now
there are 9 black balls and 5 white
balls
left in the urn. Therefore the probability that the second
ball
drawn is black, given that the ball first
drawn
is black nothing but conditional probability of F given
that
E has occurred already.
Hence
P(E/F) = 9/14
Now
by the multiplication rule of probability
P(E
n F) = P(E) × P(E/F)
=
10/15 × 9/14
=
3/7
........................................................
A
person invested Rs. 100000 in a bank FDR @ 6% p.a. for 1
year.
If interest is compounded on halfyearly
basis,
the amount payable shall be ......
a.
109060
b.
100960
c.
103090
d.
106090
Ans
– d
265
Explanation
:
Here,
P =
100000
R =
6% half-yearly = 3%@ p.a. = 0.03 p.a.
T =
1 yr = 2 half yrs
FV
= P * (1 + R)^T
So,
FV
= 100000 * (1+0.03)^2
=
106090
Ranjit
borrowed an amount of Rs. 50000 for 8 years @ 18%
roi.
What shall be monthly payment?
a.
986
b.
968
c.
896
d.
869
Ans
- a
Explanation
:
Here,
P =
50000
R =
18% = 18 % ÷ 12 = 0.015% monthly
T =
8 yrs = 96 months
EMI
= P * R * [(1+R)^T/(1+R)^T-1)]
EMI
= 50000 * 0.015 * 1.01596 ÷ (1.01596 – 1
= 986
Ajit
wants to receive Rs. 40000 p.a. for 20 years by investing
@
5%. How much he will have to invest
now?
a.
498489
263
b.
498849
c.
498948
d.
498984
Ans
- a
Explanation
:
Here,
P =
40000
R =
5% p.a.
T =
20 yrs
PV
= P / R * [(1+R)^T - 1]/(1+R)^T
PV
= (40000 ÷ 0.05) * {(1.0520 – 1) ÷ 1.0520}
=
498489
.................
Priyanka
made an investment of Rs. 18000 and he expects a
return
of Rs. 3000 p.a. For 12 years. What is
the
present value and net present value of the cash flow @
10%
discount rate?
a.
2114
b.
2414
c.
2441
d.
2141
255
Ans
- c
Explanation
:
PV
= 20441
NPV
= PV – 18000
=
Rs. 2441
The
cash flow expected from a project is Rs. 700, Rs. 1000 and
Rs.
1200 in the 1st, 2nd, & 3rd year. The
discounting
factor @ 10% roi is 1.10, 1.21 and 1.331. What is
the
total present value of these cash
flows?
a.
3264
b.
3246
c.
2346
d.
2364
Ans
- d
Explanation
:
NPV
= Σ {C÷ (1+r)T} – 1
Total
Present Value
= Σ
{C÷ (1+r)T}
=
(700 ÷ 1.1) + (1000 ÷ 1.21) + (1200 ÷ 1.331)
=
Rs. 2364
.............................................
A
10%, 6-years bond, with face value of Rs. 1000 has been
purchased
by Mr. x for Rs. 900. What is his
yield
till maturity?
a.
12.47
b.
14.27
c.
11.74
d.
11.27
Ans
- a
Explanation
:
Here,
FV
= 1000
CR
= 10%
R
(YTM) =?
T =
6 years
Coupon
= FV × CR = 100
Bond’s
price = 900
Since
FV > Bond’s Value, Coupon rate < YTM (based on above
three
observations)
So,
we have to use trial and error method. We have to start
with
a value > 10 and find the price until we
get
a value < 900.
Bond
Price = (1/(1+R)^t)((coupon*((1+R)^t-1)/R)+Face Value)
So,
If
YTM = 11%, price =957.69 (> 900, so keep guessing)
If
YTM = 12%, price = 917.78 (> 900, so keep guessing)
If
YTM = 13%, price = 880.06 (< 900, so stop)
So,
YTM must lie between 12 and 13.
So,
using interpolation technique,
YTM
=
12 + (917.78 – 900) ÷ (917.78 – 880.06)
=
12 + 17.78 ÷ 37.72
=
12.47%
.............................................
