Discussion
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 8/9th of the eligible men and 2/3rd of the eligible women claimed the gift. How much money (in Rupees) did the philanthropist give away in total?
Answer: B
The philanthropist gave away Rs 2,00,000.
Let there be \(m\) men and \(w\) women, with \(m + w = 300\). The gifts claimed are
\[ \begin{aligned} 750 \cdot \tfrac{8}{9}m + 1000 \cdot \tfrac{2}{3}w &= \tfrac{2000}{3}m + \tfrac{2000}{3}w \\ &= \tfrac{2000}{3}(m + w) \\ &= \tfrac{2000}{3} \times 300 = 200000 \end{aligned} \]
Each claiming man and each claiming woman works out to the same Rs 2000/3 per eligible person, so the split between men and women does not matter. The other amounts come from using only one group's rate for everyone or from slips in the fractions.
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