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In appreciation of the social improvements completed in a town, a wealthy philanthropist
decided to gift $Rs\; 750$ to each male senior citizen in the town and $Rs\; 1000$ to each
female senior citizen. Altogether, there were 300 senior citizens eligible for this gift. However,
only $\dfrac{8}{9}^{th}$ of the eligible men and $\dfrac{2}{3}^{rd}$ of the eligible women claimed the gift.How much
money (in Rupees) did the philanthropist give away in total?

1. $1,50,000$
2. $2,00,000$
3. $1,75,000$
4. $1,51,000$

edited | 3.2k views

Let no. of senior male be $x$
Let no. of senior female be $y$
$x + y$ = $300$

Total money given $=\left(\frac{8x}{9}\times 750= \frac{2000x}{ 3}\right) + \left(\frac{2y}{3}\times 1000= \frac{2000y}{3}\right)$

$\quad = \frac{2000}{3} \times (x +y)$
$\quad = \frac{2000}{3} \times 300$
$\quad =200000.$

So, $B$ is correct.

PS: Some people are assuming the number of senior male and female is same, which is wrong. Do not assume anything not mentioned.
by Boss (11.8k points)
edited
0
it will be (2y /3 ) x 1000  instead of  (2y /3) x750

and  if somebody  here wish to assume values of male  and female , he/she can do so

he should select the value of male  which are divisible by 9 like 180 or 90 or 270  to make calculation easy
0
@sanjay

Male: 750  ; #males = x

Female: 1000 ; #females = 300 - x

= 750 * 8/9 * x + 1000 * 2/3 * (300 - x)

= 6000x/9  + 2 * 10^5 - 2000x/3

= 2000x/3 + 2 * 10^5 - 2000x/3

= 2*10^5

Ans b)
by Boss (10.6k points)
Option B
by (259 points)

$M+F=300$

Normally, we're used to equations like $x=300$. Here, consider $M+F$ a single variable and try to manipulate the solution such that you extract $M+F$ somehow.

We need the value of

$750*\frac{8}{9}M+1000*\frac{2}{3}F$

=> $\frac{6000}{9}M+\frac{2000}{3}F$

=> $\frac{6000}{9}M+\frac{6000}{9}F$

=> $\frac{6000M + 6000F}{9}$

=> $\frac{6000(M +F)}{9}$

=> $\frac{6000(300)}{9}$

Option B

by Loyal (6.9k points)
edited