Question

A certain party consists of four different groups 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 spend?
A. Rs.2291
B. Rs.2292
C. Rs.2293
D. Rs.2294

Answer 1

Hint: Try to set up the relation between the money spent on students, politicians, actors and leaders using the given conditions.

Complete step-by-step answer:
It is given that there are 30 students, 35 politicians, 20 actors, and 27 leaders on a function day. First, make some assumptions that help to make analysis easy.
Let $S$ be the amount spent on all students, $P$ be the amount spent on all politicians, $A$ be the amount spent for all actors, and $L$ be the amount spent for all leaders.
It is given that 6 students spent as much as 7 politicians:
First, find the amount that is spent by one student and the amount spent on one politician.
The amount spent on one student is$\dfrac{S}{{30}}$ and the amount spent on one politician is$\dfrac{P}{{35}}$.
${\text{Amount spent on one student}} \times 6 = {\text{Amount spent on one politician}} \times 7$
Express the above statement in numerical form:
$\left( {\dfrac{S}{{30}}} \right) \times 6 = \left( {\dfrac{P}{{35}}} \right) \times 7$
On solving the above expression:
$\dfrac{S}{5} = \dfrac{P}{5}$
$S = P$ …(1)
It is also given that 15 politicians spent as much as 12 actors. First, find the amount that is spent by one politician and the amount spent on one actor.
The amount spent on one politician is $\dfrac{P}{{35}}$ and the amount spent on one actor is $\dfrac{A}{{20}}$.
${\text{Amount spent on one politician}} \times 15 = {\text{Amount spent on one actor}} \times 12$
Express the above statement in numerical form:
$\left( {\dfrac{P}{{35}}} \right) \times 15 = \left( {\dfrac{A}{{20}}} \right) \times 12$
On solving the above expression:
$\dfrac{{3P}}{7} = \dfrac{{3A}}{5}$
$5P = 7A$
But we already have the relation that:
$S = P$
So, substitute $S$ in place of $P$ in the equation and solve for the value of A.
$5S = 7A$
$A = \dfrac{5}{7}S$ …(2)
It is also given that 10 actors spent as much as 9 leaders. First, find the amount that is spent by one actor and the amount spent on one leader.
The amount spent on one actor is $\dfrac{A}{{20}}$ and the amount spent on one leader is $\dfrac{L}{{27}}$.
${\text{Amount spent on one actor}} \times 10 = {\text{Amount spent on one leader}} \times 9$
Express the above statement in numerical form:
$\left( {\dfrac{A}{{20}}} \right) \times 10 = \left( {\dfrac{L}{{27}}} \right) \times 9$
On solving the above expression:
$\dfrac{A}{2} = \dfrac{L}{3}$
$3A = 2L$
Since it is already analyzed that:
 $A = \dfrac{5}{7}S$
Therefore, the above relation is given as:
$3 \times \dfrac{5}{7}S = 2L$
$L = \dfrac{{15S}}{{14}}$ …(3)
It is given that the total amount spent on the party is Rs. 9000.
Express the above statement in numerical form:
$S + P + A + L = 9000$
Substitute $P = S,A = \dfrac{{5S}}{7},L = \dfrac{{15S}}{{14}}$ in the above expression:
$S + S + \dfrac{{5S}}{7} + \dfrac{{15S}}{{14}} = 9000$
On solving the above expression for$S$ :
$\dfrac{{14S + 14S + 10S + 15S}}{{14}} = 9000$
$\dfrac{{53S}}{{14}} = 9000$
On cross multiplication:
$S = \dfrac{{9000 \times 14}}{{53}}$
$S = 2290.90$
Round it to the nearest rupees:
$S = 2291$
Therefore, the amount spent on students is Rs.2291.

Therefore the option A is correct.

Note: Try to find all the relation of $P,L$ and$A$ in terms of S, so that we can use them in the last to find the value of S using the relation that the total amount spent on the party is Rs. $9000$.