CBSE Class 12-commerce Answered
Table below shows the symbols considered for Male and female students of each course
BA | BSc | BCom | ||||
Year | Male | Female | Male | Female | Male | Female |
I | a | b | c | d | e | f |
II | g | h | i | j | k | l |
III | m | n | o | p | q | r |
Above Table shows 18 unknown variables . Hence we need 18 equations to be formed
from 18 given information. Then solve these 18 equations to get all the unknowns .
⇒ Information #1 :- total number of students (male+female ) of all courses = 2000 .
⇒ Information #2 :- Total Female students greater than total male students by 60.
From above informations, we get the following two equations.
b + h + n + d + j + p + f + l + r = 1030 .........................(1)
a + g + m + c + i + o + e + k + q = 970 ........................(2)
⇒ information #3 :- BA students of all year = 36 % = (36/100) × 2000 = 720
a+g+m+b+h+n = 720 ................................(3)
⇒ information #4 :- B.Com students of all year = 30.5 % = (30.5/100) × 2000 = 610
e + k + q + f + l + r = 610 ................................(4)
⇒ information #5 :- From information # 4 and #5 , we get B.Sc students of all year = (100-36-30.5) % = 33.5 %
B.Sc students of all year = (33.5/100) × 2000 = 670
c + i + o + d + j + p = 670 ................................(5)
⇒ information #6 :- 32% of students are in first year
Number of students in first year = ( 32/100) × 2000 = 640
a + b + c + d + e + f = 640 ..........................(6)
⇒ information #7 :- Number of students in second year is 100 more than those of second year .
From known value of total students , i.e. 2000 and from information #6 and #7 , we get
Number of students in second year = 730
Number of students in third year = 630
Hence we get
g + h + i + j + k + l = 730 ...............................(7)
m + n + o + p + q + r = 630 ........................(8)
⇒ information #8 :- 30 more females in BA than number of females in B.Com
b + h + n - f - l - r = 30 ..........................(9)
⇒ information #9 :- 20 less females in B.Sc than number of females in B.Com
f + l + r - d - j - p = 20 ........................(10)
by adding eqn.(9) and (10) , we get
b + h + n - d - j - p = 50 .........................(11)
By adding (1) and (9) , we get
2( b + h + n ) + d + j + p = 1060 .........................(12)
By solving eqn.(11) and (12) , we get
(b+h+n) = 370 ...........................(13)
(d+j+p) = 320 ............................(14)
By substituting d+j+p) in (11) , we get
(f+l+r) = 340 ..........................(15)
Using information about female students from eqn.(13), (14) and (15) , we get the following information
of male students from eqn.(3) , (4) and (5)
a + g+ m = 350 ................................(16)
e + k + q = 270 ................................(17)
c + i + o = 350 ................................(18)
⇒ information #10 :- Ratio of BA male students in first year to those in third year = 8 : 7
a : m = 8 : 7 or m = (7/8) a ..............(19)
⇒ information #11 :- second year BA male students are greater by 5 tan those in first year
g = a + 5 ..........................(20)
Using eqn.(19) and (20) , we rewrite eqn.(16) as
a + a+5 + (7/8)a = 350
From above expression, we get a = 120 .
By substituting a in eqn. (19) and (20) , we get m = 105 and g = 125 .
⇒ information #12 :- second year BA male students and second year BSC male students are equal
Hence we get , i = g = 125
⇒ information #13 :- First year B.SC male students are greater than those of third year by 5
Hence we get , c = o + 5
Hence we rewrite eqn.(18) as
o+ 5 + 125 + o = 350
From above expression we get o = 110
hence , c = 115
⇒ information #14 :- second year femal BA students= second year male B.Com students
Hence, we get , h = k ................... (21)
⇒ information #15 :- second year femal BSC students= second year male B.Sc students
Hence , we get j = i = 125 .................(22)
⇒ information #16 :- Female students of second year B.com and second year B.Sc are equal
Hence, we get , j = l ........................(23)
From eq.(22) and eqn.(23) , we get l = 125 ...................(24)
⇒ information #17 :- In B.Com Each number of first year male students and female students is less than respective third year students by 5
From above information, we get
q - e = 5 ....................................(25)
r - f = 5 ....................................(26)
⇒ information #18 :- Female students in B.Sc Third year is 100
p = 100 ...................(27)
By substituting p from eqn.(26) and substituting j from eqn.(22) , we get d from eqn.(14) as
(d+125+100) = 320
d = 95 ...................(28)
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By substituting l from eqn.(24) and f from eqn. (26) , we rewrite eqn.(15) as
(f+l+r) = ( f+125+f+5 ) = 340
From above expression, we get f = 105
Hence r = 110 .....................(29)
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Let us consider eqn.(7)
g + h + i + j + k + l = 730 ...............................(7)
in above expression , except h and k all other values are known .
Hence from above expression, by substituting relevant values ,
we get equation for h and k .
125 + h + 125 + 125 +k + 125 = 730
h + k = 230
From eqn.(21) h = k
Hence h = k = 115 .........................(30)
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Let us consider eqn.(17)
e + k + q = 270 ................................(17)
if k = 115 ( eqn.30) , then q + e = 155
From eqn.(25) , q - e = 5
By solving above equations in e and q , we get
q = 80 ..................................(31)
e = 75 ............................(32)
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Let us consider eqn. (6)
a + b + c + d + e + f = 640 ..........................(6)
In above expression , except b all other values are known .
Hence from above expression, by substituting relevant values ,we get b
120 + b + 115 + 95 + 75 + 105 = 640
b = 130 .............................(33)
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Let us consider eqn. 913)
(b+h+n) = 370 ...........................(13)
bu substituting values of b and h , we get n
130 + 115 + n = 370
n = 125
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numbers of students in all the courses are known and the values are tabulated below
B.A | B.Sc | B.Com | ||||
Male | Female | Male | Female | Male | Female | |
I year | 120 | 130 | 115 | 95 | 75 | 105 |
II Year | 125 | 115 | 125 | 125 | 115 | 125 |
III Year | 105 | 125 | 110 | 100 | 80 | 110 |