Question

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 ?

• A. Rs . $2291$
• B. Rs . $2292$
• C. Rs . $2293$
• D. Rs . $2294$

Answer 1

The correct option is A Rs . $2291$

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.

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 $\times 6=$ Amount spent per politician $\times 7$

OR, (Total amount spent on students / Total students)$\times$ 6 = (Total amount spent on politicians / Total politicians) $\times$7

Or, $(S/30\times 6=(P/35)\times 7$

$\Rightarrow S/5=P/5$

$\Rightarrow S=P$..........(i)

15 politicians spent as much as 12 actors:

Therefore, $\left(P/35\right)\times 15=\left(A/20\right)\times 12$

$\Rightarrow 3P/7=3A/5$

$5P=7P$

$5S=7A$ (since $S=P$)

$A=5S/7$............(ii)

and 10 actors spent as much as 9 leaders:

Therefore, $\left(A/20\right)\times 10=\left(L/27\right)\times 9$

$3A=2L$

$A=2L/3$

$5S/7=2L/3$ (since $A=5S/7$)

$L=15S/14$...........(iii)

Total amount spent for the party is Rs. $9000$.

i.e. $S+P+A+L=9000$

Using eq (i), (ii) and (iii), we get

$S+S+5S/7+15S/14=9000$

$53S/14=9000$

$S=9000\times 14/53$

$S=2290.90$

Hence, the answer is Rs. $2291$.