Unit - I PARTNERSHIP
Partnership is a business where two (or more)
partners invest a certain amount (known as capital) for a specific period to
carry out the business. At the end of the period (usually one year), the
business may generate profit or loss. This profit or loss is divided among the
partners in the ratio of their investments.
If A and B are in partnership, at
the end of one year (which is convention), the profit or loss would set
distributed as:
Profit (or
loss) = (Capital invested) × (Period of investment)
NOTE:
1. A partner
retires during one year period: - in such case, only the period for which his
capital was utilized, is taken into confederation.
2. A partner
joins during the one year period: - in such case, only the period for which his
capital was utilized, is taken into confederation.
EXAMPLE:
1. A and B
started a business in partnership by investing Rs.8000 and Rs.7000
respectively. If at the end of a year, a profit of Rs.22, 500 was earned, what
is the share of A?
Solution:
Ratio of
amount inverted by A and B = 8000: 7000
= 8:7
Profit at
the end of the year =
Rs.22500
Share of A
=8/15x22500=8x1500 = Rs.12000/-
2. In
partnership business, A has inverted Rs.4200 while B has inverted a certain
amount. If out of the overall profit of Rs.600, A’s share is Rs.320, what is
the amount inverted by B (in Rs)?
Solution:
A’s investment = Rs.4200
Overall profit = Rs.600
A’s share in
profit = Rs.320
:. B’s share
in profit = Rs.600-
Rs.320=Rs.280
The ratio of
profit of A and B = 320: 280= 8:7
:. The
amounts inverted by A and B will be in the ratio Of 8:7
Rs. 4200: B’s
investment =8:7
ð B’s investment = 7x4200/8= Rs.3675
3. chetan
and suman started a business in partnership by investing Rs.15000 and Rs.18000
respectively. If at the end of the year, chetan’s share in the profit was
Rs.1200, what was the amount of total profit?
Solution: If Rs.15000 earns a profit of Rs.1200, then
Rs.33000 earn a profit of 33000x1200/15000=2640.
4. In a
partnership business, A has inverted 2000 for 5months, while B has invested
Rs.3500 for a certain period. If out of the total annual profit of Rs.1440, B’s
share has been Rs.840, for how many months has he kept his investment in the
business?
Solution:
A has
invested Rs.2000 for 5 months
B has
invested Rs. 3500 for ‘m’ months.
Total profit
at the end of the year= Rs.1440, B’s share in it is= RS.840
A’s share in
profit = Rs. (1440-840) =Rs.600
The ratio of
profit of A and B = 600:840=5:7 The ratio of investment of A and B is the same
as that of the profits
2000x5/3500x5=5/7
:. m=
7x2000x5/3500x5=4
Hence, B
kept the investment for 4 months only.
Practice:
- A started business with an
investment Rs.6000. four months later, B joined him with his investment
Rs.60000. If at the end of the year Rs. 35000 profit is made, what is the
share of A in the same?
a) Rs.14000 b) Rs.21000
c) Rs.15000 d) Rs.20000 e) none of these
Ans:
b) Rs.21000
- A and b invest Rs 3000 and Rs.
2000 respectively in a business. A was a sleeping partner. At the end of
the month, both set Rs.150 each. What was B’s remuneration for his work?
a) Rs.60 b) Rs.40
c) Rs.50 d) Rs.30 e) None of
these
Ans: c) Rs.50
DATA
INTERPRETATION AND ANALYSIS
Directions (1-5) : study the following table
and answer the questions that follow:
The table
shows the percentage of unemployed male and female youths and the total
population of different states in two years.
|
State
|
2008
|
2009
|
||||
|
M
|
F
|
T
|
M
|
F
|
T
|
|
|
P
|
11
|
16
|
35
|
9
|
11
|
39
|
|
Q
|
9
|
7
|
19
|
10
|
8
|
24
|
|
R
|
8
|
11
|
25
|
10
|
13
|
41
|
|
S
|
12
|
6
|
30
|
7
|
7
|
34
|
|
T
|
7
|
6
|
32
|
5
|
6
|
24
|
|
U
|
8
|
5
|
26
|
8
|
9
|
35
|
M-
percentage of unemployed male youth over total population
F-
percentage of unemployed female youth over total population
T- Total
population of the state in lakhs.
1) what was
the total number of unemployed youths in state Q in 2009?
a)
351000 b) 447000 c)432000 d) 521000 e)
none
Ans: c) 432000
The
percentage of unemployed male youths in state Q in 2009 is 10% and the
percentage of unemployed female youths in state Q in 2009 is 8%. Thus , the
total number of unemployed youths in 2009 in state Q will be (10+8) = 18% of the total population.
The total
population of state Q in 2009 is 24 lakhs
:. The number of unemployed youths
in state Q in 2009 :- 18/100x24 lakhs = 4.32 lakhs = 432000
2. How many
female youths were unemployed in state T in 2008?
a)
192000 b) 241000 c) 224000
d) 301000 e) none.
Ans: a) 192000
The
percentage of unemployed female youths in state T in 2008 is 6%. The total
population of state T in 2008
6/100x32lakhs =1.92lakhs =192000
- what was the difference between
the no. of unemployed male youths in state s in 2008 and 2009 ?
a) 109000
b) 122000 c) 212000 d) 98000 e)
none
Ans : b) 122000
The number
of unemployed male youths in state s in 2008 =12% of 30lakhs
=12/100x30lakhs
= 3.6lakhs= 360000
The no of unemployed male youths in state S in 2009 = 7% of
34lakhs
= 7/100x34lakhs =
2.38lakhs = 238000
:. The required difference = 360000 -238000 = 122000.
- What was the respective ratio of the unemployed male youths in state P in 2008 and state R in 2008
a)
11:47 b)
23:49 c) 52:47 d)
2:3 e) none of these
Ans : e) none of
these
The no of unemployed male youths
in state P in 2008 = 11% of 35lakhs
=11/100x35lakhs = 3.85lakhs =385000.
The no of unemployed male youths
in state R in 2008 = 8% of 25lakhs
= 8/100x25lakhs =2lakhs =200000
:. The required ratio = 385000 =
200000 = 77:40
As the answer is not given in any
of the assume options, the answer is (2).
- The no. of unemployed female youths in state (4) u in 2008 is ap0proxiamately what percent of the no of unemployed female youths in state U in 2009?
a)
20% b)
35% c) 55% d) 40% e) none
Ans:
d) 40%
The no of unemployed female youths in state U in 2008 = 5%
of 26 lakhs
=5/100x26lakhs= 1.30lakhs -130000.
The no of employed female youths in state U in 2009 = 9% of
35lakhs
=9/100x35lakhs = 3.15lakhs = 315000.
130000 = x/100x315000
X= 130000 x 100 / 315000 = 41.27% = 40%
||. Directions
(Q.no.6-10) : Study the following pie-charts and answer the questions that
follow.
The pie chart shows the percentage of various products
produced.
The following Pie chart shows the income obtain selling the
product.
Total income obtained by selling all the products = Rs. 50
million.
- If the expenditure incurred in production of product N per tonne was Rs. 5000, what was the percent profit earned ?
a)
15% b)
25% c) 55% d) 45% e) none of these
- what is the approximate per selling price of all the six products together ?
a)
Rs 14,320 b) Rs. 15770 c)Rs.16670
d) data in adequate e) none of
these.
- Which product has got the highest selling price per tonne ?
a)
product L
b) product M c) product N d) product O e) none of these
- What is the selling price of product Q per tonne?
a)
Rs 21800 b) Rs.23450 c) RS.19760
d) Rs. 24740 e) none
- If the quantity of product N produced increased by 20% in the next year and selling price per tonne remains the same, then what would be the income generated by selling product N in the next year ?
Explanation (6-10)
|
Product
|
Quantity of Product
Produced in Tonnes
|
Income obtained
By Selling the Product
|
Income obtained per Tonnes
|
|
L
|
510
|
1,50,00,000
|
Rs. 29,411.76
|
|
M
|
420
|
60,00,000
|
Rs. 14,285.71
|
|
N
|
480
|
30,00,000
|
Rs. 6,250
|
|
O
|
360
|
50,00,000
|
Rs. 13,888.89
|
|
P
|
720
|
70,00,000
|
Rs. 9,722.22
|
|
Q
|
510
|
1,40,00,000
|
Rs. 27,450.98
|
6) (b) 25%
The expenditure incurred in production of product N is Rs.
5000 per tonne
The income obtained by selling products N per Tonne =
3000000/480 = 6250
As can be seen, the profit obtained per tanne by selling
product N:-
=6250 –
5000 = 1,250.
:. The required percentage profit :-
1250/5000x100 = 25%
7) © Rs.16670
Total quantity produced=3000 tonnes
Total income obtained = Rs.50 million
Selling price per tanne = 50000000/3000 = Rs 16666.67
~ Rs. 16670
8. a) product L
As can be seen from
the table above, the selling price of product Q is Rs. 27450 per tanne. As the
answer is not given in any of the options.
- d) Rs. 3600000
The quantity of
product N produced = 480 tanned The quantity produced in the next year :
120/100x480 = 576 tannes
Per tanne selling price of product N remains the same i.e.
Rs. 6250.
:. Amount obtained by selling N in the next year =6250 x 576
= 3600000.
UNIT |||
AVERAGE AND PROBLEMS ON AGES
Average is a very
simple but effective way of representing an entire group by a single value.
Average of a group is defined as
Average = sum of all items in the group / no of items in the group
If the value of each
item is increased by the same value ‘p’ then the average of the group or items will also
increase by p.
If the value of each item is decreased by the same value ‘p’ then the average of the group or
items will also multiply by ‘p’.
If the value of each item is divided by the same value p
(p#0), then the average of the group or items will also be divided by p
The average of group0 of items will always lie between the
smallest value in the group and largest value in the group i.e., the average
will be grater than the smallest value and less than the largest value in the
group.
Allegation rule :
This states that “ when different quantities of the same or
different ingredients, of different costs (one cheap and the other dear) are
mixed together to produce a mixture of a mean cost , the ratio of their
quantities are inversely proportional to the difference in their cost from the
mean cost “
Quantity of cheap/
Quantity of dear = price of dear –mean price/ mean price – price of mean
Average value : These are four different means.
1)
arithmetic mean 2) harmonic mean 3) geometric
mean 4) weighted mean
Examples :
- find the average of all prime numbers between 30 and 50.
Solution : the prime numbers between 30 and 50 are :
31,37,41, 43 and 47
:. Required average
= 31+37+41+43+47/5 =199/5 =39.8
- The average age of a class of 39 students is 15 years if the age of the teacher be included, then the average increases by 3 months. Find the age of the teacher.
Solution: Total age of 39 persons = (39x15) years = 585
years
Average age of 40 persons = 15 years 3months
=61/4 years
Total age of 40persons = 61/4x40 years
=
610 years
:. Age of the teacher
= (610-585) years = 25 years.
- Distance between two stations A and B is 778 km. Han covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56 km per hour. Find his average speed during the whole journey.
Solution : Required
average speed
=
2xy/x+y km/hr ( harmonic mean)
= 2x84x56
/ 84+56 km/hr
=
(2x84x56) /140 km/hr = 67.2 km/hr.
- A batsman makes a score of 87 runs in the 17th innings and these increases his average by 3. find the average after 17th innings.
Solution : Let the
average after 17th innings =x
Then. Average
after 16th innings = (x-3)
:. 16 (x-3) + 87 = 17x
=> x= 87-48=39
5. The average age of the husband , his wife and their sons
ten years ago was 25 years and that of the husband and wife six years ago was
37 years. What is the present ages of son ( in years ) ?
Solutions : Total of present ages of husband, wife and son =
(25x3) +10+ 10 +10 = 105 years.
Average age of husband and
his wife six years ago was 37 years
Total of present ages of husband and wife = (37x2) +6 +6 =
86 years.
:. Son’s present age = 105 – 86 = 19 years.
- The average age of A and B is 30 years. If c were to replace A, the average age would be 40 years and if he were to replace B, the average age would be 35years. What is A’s age?
Solutions :
Average age of A and B = 30 years
Total age of A and B = 30x2 = 60 years
Average age of B and C = 40 years
Total age of B and C = 40x2= 80 years
Total age of A and c
= 35x2 = 70 years
After adding (1) and (3) we get
2 A + B + C = 130
But we know that (B+C) = 80
:. 2A + 80 = 130
A = 130 – 80/2 = 25
years.
Hence, a’ s age is 25 years.
Practice:
1.
Ram secured 50,50 and 60 marks in 3 out of 4 papers. If he secured 50
members in aggregate, how many marks did he secure in the fourth paper?
a)
40 b) 45
c) 50 d) 55 e) none of these
Ans a) 40
2.
A father is now 7 times older than his son but
two years hence he will be only five times older. What is the father’s present
age (in years)?
a) 28 b) 30
c) 31 d) data inadequate e) none of these
Ans a)
28.
Dr. D.Giri
Reader in Statistics
S.V.A. Govt college (M)
SRIKALAHASTI -517644,
Mobile : 9703102294
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