Latest HCL Aptitude Question SOLUTION: A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party memb

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A certain party consists of four different group of people - 30 students, 35 politicians, 20 actors and 27 leaders. On a particular function day, the total cost spent on party members was Rs.9000. It was found that 6 students spent as much as 7 politicians, 15 politicians spent as much as 12 actors and 10 actors spent as much as 9 leaders. How much did students spent?

Asked In HCL sushmita (11 years ago)

Solved swati singh Read Solution (6)

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Read Solution (6) :

swati singh  (11 years ago)

as question says,
30s+35p=20a+27L =9000 say eqn 1
6s=7p , 15p=12a , 10a=9L
or
6s=7p , 7p=(12*7)/15 a =(28/5)a , (28/5)a= (28/50)*9L
OR
6s=7p=(28/5)a=(252/50)L = K
now

s=(k/6), p= (k/7) , a=(.1785k) , L=(.1984k)
put these value in eqn one you will got value of k is 475.511
now 6s=k
hence s=k/6=79.25
there are 30 students hence 79.25*30=2377.55

Is this solution Helpfull? Yes (26) | No (6)  

sushmita  (11 years ago)

thnkx swati :)

Is this solution Helpfull? Yes (5) | No (1)  

kowsalya devi  (11 years ago)

hai swati can you explain this problem once again?how 28/5 came

Is this solution Helpfull? Yes (4) | No (1)  

swati singh  (11 years ago)

sry sweta eqn one is 30s+35p+20a+27L = 9000

Is this solution Helpfull? Yes (3) | No (1)  

tejaswi andekar  (10 years ago)

Solution:

Let S be the amount spent for all students
Let P be the amount spent for all politicians
Let A be the amount spent for all actors and
Let L be the amount spent for all leaders.
given that 6 students spent as much as 7 politicians

i.e Amount spent per student x 6 = Amount spent per politician x 7
Or (Total amount spent on students / Total Students) x 6 = (Total amount spent on politicians / Total politicians)x 7
Or., (S/30)x 6 = (P/35)x7
=> S/5 = P/5

=> S = P ..... eqn 1

15 politicians spent as much as 12 actors :
Therefore, (P/35)x15 = (A/20)x12
=> 3P/7 = 3A/5
=> 5P = 7P
=> 5S = 7A (since S = P)

=> A = 5S/7 ........eqn2

and 10 actors spent as much as 9 leaders :
Therefore, (A/20)x10 = (L/27)x9
=> 3A = 2L
=> A = 2L/3
=> 5S/7 = 2L/3 (since A=5S/7)

=> L = 15S/14 ......eqn3

the total amount spent for the party is Rs.9000
i.e., S+P+A+L = 9000
from eqn1, eqn2, eqn3 we have
S + S + 5S/7 + 15S/14 = 9000
53S/14 = 9000
s=9000*14 / 53
s=2290.90 ~ 2291

Hence the answer is Rs.2291

Is this solution Helpfull? Yes (2) | No (2)  

samuel  (7 years ago)

Let S be the amount spent for all students
Let P be the amount spent for all politicians
Let A be the amount spent for all actors and
Let L be the amount spent for all leaders.
given that 6 students spent as much as 7 politicians

i.e Amount spent per student x 6 = Amount spent per politician x 7
Or (Total amount spent on students / Total Students) x 6 = (Total amount spent on politicians / Total politicians)x 7
Or., (S/30)x 6 = (P/35)x7
=> S/5 = P/5

=> S = P ..... eqn 1

15 politicians spent as much as 12 actors :
Therefore, (P/35)x15 = (A/20)x12
=> 3P/7 = 3A/5
=> 5P = 7P
=> 5S = 7A (since S = P)

=> A = 5S/7 ........eqn2

and 10 actors spent as much as 9 leaders :
Therefore, (A/20)x10 = (L/27)x9
=> 3A = 2L
=> A = 2L/3
=> 5S/7 = 2L/3 (since A=5S/7)

=> L = 15S/14 ......eqn3

the total amount spent for the party is Rs.9000
i.e., S+P+A+L = 9000
from eqn1, eqn2, eqn3 we have
S + S + 5S/7 + 15S/14 = 9000
53S/14 = 9000
s=9000*14 / 53
s=2290.90 ~ 2291

Hence the answer is Rs.2291

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