PROCUC SYSTEM
Please, mathematicians and economists, try to solve these questions
Some of the Questions that are found in the Procuc System book
Qn .1
The payment made per day for a certain amount of money deposited in a bank account of Mr.Onyango by Mr.Mwaipaja as a result of poculization is Tshs. 2600/= for a nine month proeperio. The amount paid by Mr. Onyango per day persuaded Mr Tewele and Mr.Ngowi to deposit in the bank Tshs. 700,000/= and Tshs. 800,000/= respectively for the purpose of poculization at the same Poculization Agreement. Procuc Operator Financial Capital, Electronic Fiscal Device Reading, Customer’s Financial capital Percentage per Day, Customer’s Financial income Percentage, Customer’s Financial gain Percentage Aid and Exceeding Days per proeperio are Tshs. 3,000,000/=, Tshs. 10,834,000/=, 0.52%, 5%, 45.4% and four(4) respectively. In accordance with the Revenue Authority, where turnover exceeds Tshs.3,000,000/= but does not exceed Tshs.7,000,000/= and where turnover exceeds Tshs.7,000,000/= but does not exceed Tshs. 14,000,000/= Net Taxes payable are Tshs. 95,000/= and Tshs. 291,000/= respectively. Use this information to answer the following questions:
a) Calculate the Gross Financial Gain of Mr.
i) Mwaipaja
ii) Tewele
iii) Ngowi
b) Find the Gross Financial Gain of Mr. Onyango
i) Obtained as a customer due to his financial capital
ii) Due to his financial capital as profit
c) (i) Give the Total Gross Financial Gain of Mr.Onyango
(ii) Give the Grand Total Gross Financial Gain of Mr.Onyango
d) Calculate the :
i) Procuc Operator Rough Turnover
ii) Procuc Operator Actual Turnover
iii) Procuc Operator Rough Net Income
iv) Procuc Operator Actual Net Income
Qn.2
Mr. Kikando deposited Tshs. 500,000/= in Mr. Alexander’s bank account for the purpose of Poculization for the ninemonth proeperio. The Customer’s Financial income per Day, Customer’s Financial gain Percentage Aid, Customer’s Gross Financial Gain percentage, Pocu Gross Financial Gain and Exceeding days are Tshs.2600/=, 45.5%, 47.48%, Tshs.487,400/= and four respectively. Mr. Alexander prepared the Selling Price Table below in order to choose the best selling price which does not bring unwarranted nuisance in terms of change at each Commodity Flow Figure.
n

CFF

FSP in Tshs

SSP in Tshs

PCSS

5

0.03125

515,200

515,210

2

4

0.0625

530,460

530,500

2

3

0.125

560,900

560,930

2

2

0.25

621,850

621,900

2

1

0.5

743,700

743,700

2

0

1

987,400

987,400

1

Use the details above to answer the following questions:
(a) Graphically determine the POCU percentage by;
(i) Probu method
(ii) Computable Cuncialtag method
(iii) Proficug method
(iv) Cocuncialhalf method
(v) Pogronancialhalf method
(b) Graphically determine the buying price of the cost object by Pocufigaper method.
Qn.3
An amount of money worth Tshs.500,000/= was deposited in the bank account of Mr. Joseph Richard by Mr. Josephat C. Njige for running Procuc at %CFPD and %CFPA of 0.52% and 45.4% respectively. The Poculization Agrement between Mr. Joseph Richard and Mr. Josephat C. Njige ceased to exist in 274 days. Calculate the percentage that determined the cost objects selling price and Gross Financial Gain of Mr. Joseph Richard and Mr. Josephat C. Njige.
Qn.4
In order to meet financial exigency, Mr, Malulu deposited Tshs.500,000/= as contribution to Procuc in the bank account of Dr. Msimu on 28^{th} October, 2011. The Poculization Agreement was for a ninemonth proeperio, starting on 1^{st} November, 2011 to 1^{st} August, 2012 at 0.52% as %CFPD and 5% as %CFP. Unfortunately, Mr.Malulu’s daughter called Neema got sick. The horrendous situation of Neema’s health necessitated the earliest withdrawal of capital from Procuc. Mr.Malulu decided to withdraw his financial capital from Procuc on 1^{st} January, 2012 due to the fact that he was terribly sad about his daughter’s horrific condition. The withdrawn amount allowed Neema to be on medication. Use this information to answer the following questions.
(a) Calculate Mr. Malulu’s
(i) Gross Financial income
(ii) Financial capital Loss
(iii) Financial capital percentage Loss
(iv) Remained Approximated percentage figure
(b) Use the following formula to calculate Mr. Malulu’s Indemnity.
CI=CGF/d + d (RA × CGF)
Given that, d=12
Where CI, CGF, d and RA stand for Customer’s Indemnity, Customer’s Gross Financial income, flomarcosh fixed value and Remained Approximated percentage figure respectively.
(c) Calculate the Indemnity percentage of Mr. Malulu.
(d) The product of Cuinde and 100, gives %CI.
Mathematically, it is expressed as:
%CI = Ci ×100. Using this equation, show that,
CI=(%CI × CGF)/(100%CI)
where %CI and Ci stand for Customer’s Indemnity percentage and Cuinde respectively
(e) Show how the following formula is derived:
%CI = 100(1 + (d^{2 }× RA))/( d + (d^{2 }× RA) +1)
where = stands for is not equal to
Qn.5
Mr. Migilimo deposited a certain amount of money in Mr. Marco’s bank account as the Principal for poculization in Procuc System for a nine monthproeperio (from November2011 to July2012). He also found Mr. Punguja at the bank depositing the amount of Tshs.300,000/= in Mr. Marco’s account for the same purpose. The Gross Financial Gain percentage of Mr. Migilimo is 47.48% and the Exceeding Days per proeperio were four. By referring to these details, answer the questions that follow.
(a) Who
(i) is a Procuc Operator?
(ii) are Customers?
(b) (i) How many days were spent up to Proeperio date?
(ii) Give the difference between the days which were spent up to Proeperio date
and the exceeding days.
(iii) Determine the exceeding days spent up to Proeperio date.
(c) Calculate:
(i) the amount deposited by Mr. Migilimo in the bank account, given that, Gross Financial Gain and Financial income per Day of Mr. Migilimo is Tshs.237,400/= and Tshs.2,600/= respectively. Note that his Financial gain Percentage Aid is 45.4%
(ii) the Financial capital Percentage per Day of Mr. Punguja and Mr. Migilimo
(iii) the Financial income Percentage of Mr. Punguja and Mr. Migilimo
(d) What will be the:
(i) Gross Financial income of Mr.Migilimo after the stipulated period?
(ii) Monthly pay of Mr. Migilimo?
(iii) Monthly pay of Mr.Punguja?
(iv) Financial capital Withdrawn Amount of Mr.Punguja?
(v) Financial capital Withdrawn Amount of Mr. Migilimo?
(e) How much will Mr.Punguja get as his
(i) Gross Financial Gain?
(ii) Gross Financial income?
(f) Who will be economically ahead among the two? If so, why?
Qn.6
Emmanuel J. Mwininga deposited Tshs.500,000/= in the Bank account of George Peter Balole as contribution to Procuc at 0.52% as % CFPD. Tshs 2,600/= as CFD enthusiastically enticed Emmanuel J. Mwininga away from other Procuc Operators. Use this information to answer each of the following questions:
a) Who is
(i) a creditor
(ii) a debtor?
b) Give the synonym of creditor and debtor as far as Procuc System is concerned.
c) Complete the table below by filling in the Customer’s Financial Payment (CFP) at each given CFT.
TND

y

ITND

CFT

CFP

8.6

2

7

1Week
 
17.2

3

14

2weeks
 
34.25

4

30

1 Month
 
68.5

9

60

2 months
 
137

17

120

4 Months
 
274

4

270

9Months

d) Show that, the Exceeding Days of 34.25, 68.5 and 137 days are 4, 9 and 17 days respectively.
Qn 7
Three Procuc Operators, namely, John Daudi, Dickson Charles and Flora Peter Marco were using different Customer’s Financial capital Percentage per Day as poculization rate. Mwajuma Hamis deposited Tshs.500,000/=, Tshs.300,000/= and Tshs.200,000/= in the bank accout of John Daudi, Dickson Charles and Flora Peter Marco respectively for poculization purpose. Kisoka and Mtawa Amos decided to deposit their money in the bank account of Procuc Operators for the same purpose. Kisoka deposited Tshs.450,000/=, Tshs.500,000/= and Tshs.800,000/= in the bank account of Dickson Charles, Flora Peter Marco and John Daudi respectively. Mtawa Amos deposited Tshs.1,000,000/=, Tshs.300,000/= and Tshs.400,000/= in the bank account of Flora Peter Marco, John Daudi and Dickson Charles respectively. 5%, 4% and 6% are the %CFP which were used for poculization by John Daudi, Dickson Charles and Flora Peter Marco respectively. Poculization Agreement ceased to exist in 274days. Mtawa Amos obtained his Gross Financial income of Tshs.384,900/=, Tshs.1,375,200/= and Tshs.564,000/= from John Daudi, Flora Peter Marco and Dickson Charles respectively. Tshs.687,600/=, Tshs.634,500/= and Tshs.1,026,400/= were obtained by Kisoka as his Gross Financial income from Flora Peter Marco, Dickson Charles and John Daudi respectively. Mwajuma Hamis obtained Tshs.423,000/=, Tshs.641,500/= and Tshs.275,040/= as her Gross Financial income from Dickson Charles, John Daudi and Flora Peter Marco respectively. Use this information to attempt the following questions:
a. Find the Customer’s Financial capital Percentage per Day which was used for conducting poculization for each Procuc Operator
b. Determine
i. %CFPA for each Procuc Operator
ii. The exceeding days per proeperio
c. Calculate the Net Income of
i. Mwajuma Hamis
ii. Kisoka
iii. Mtawa Amos
Given that, MP = 2.95%, where MP stands for Mutable Percentage.
d. Calculate the Mutable Amount (MA) of Procuc System Team.
Qn. 8
(a) Show that,
b = log_{10}[(1+TP)  %CFPD× TND) + %CFP]
(b) Given that, TP = 57%, %CFPD = 0.52%, TND = 274 days and %CFP = 5%
(i) Give the actual value of 10^{b }
(ii) Prove that, log_{10}[(1+TP)  %CFPD× TND) + %CFP] = 0.978636948%
Where, TP stands for Tiocalization Percentage
%CFPD stands for Customer’s Financial capital Percentage per Day
TND stands for Total Number of Days
%CFP stands for Customer’s Financial income Percentage
b stands for tiocalization exponent
Qn.9
Given that,
log_{10}2=0.301029995,
k^{ℓ} =0.602059991,
xlog_{10}2= log_{10}y and mlog_{10}2= log_{10}yk^{ℓ}, where m=1.169925001.Use the given information above to answer the following items.
(a) Find the value of x
(b) Find the value of log_{10}9 without using tables or calculators and correct the answer to 4 decimal places.
(c) Find the value of log_{10}4096 without using tables or calculators and correct the answer to 4 decimal places.
Qn.10
(a). Given that, log_{10}2=0.301029995, 2x=10^{y }and 2m =10^{y} k^{antiℓ }
(i). If m = 498, what will be the value of x?
(ii). Prove that, 10^{y}=1000^{ }
(iii).Find the value of k^{antiℓ}
(b) Find the value of k^{ℓ}, given that, k^{ℓ}=2 log_{10}2
(c).Without using tables or calculators, prove that log_{10}3 = 0.4771,
where, m = 0.41503737499.
Qn. 11
Given that,
log_{10}2=0.301029995,
k^{ℓ} =0.602059991,
k^{v} =3.612359948,
xlog_{10}2= log_{10}y and mlog_{10}2= log_{10}yk^{v}, where m= 9.192645078.Use the given information above to answer the following items.
(a) Find the value of x
(b) Find the value of log_{10}7 without using tables or calculators and correct the answer to 4 decimal places.
Qn.12
(a). Given that, log_{10}2=0.301029995, k^{antiℓ }=4, k^{antiv} = 34,
2x=10^{y }and 2m =10^{y} k^{antiv }
(i). If m = 14, what will be the value of x?
(ii). Prove that, y= log_{10}6
(b). Find the value of y without using tables or calculators, where, m=18.4150375, k^{ℓ} =0.602059991and
k^{v}=6.321629909.
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