GATE CS 2018 Q.6 (GA Q.6): Quantitative Aptitude

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?

1,50,000

2,00,000

1,75,000

1,51,000

Official answer and solution

Official answer: B
From: Official GATE 2018 answer key

Solution

Formulate the total expenditure using the number of eligible men and women, noticing the identical effective rate per person.

Let $M$ be the number of eligible male senior citizens and $W$ be the number of eligible female senior citizens. We are given $M + W = 300$ .

The number of men who claimed the gift is $\frac{8}{9}M$ , each receiving Rs 750.
The total amount given to men is:

\text{Amount}_{\text{men}} = 750 \times \left(\frac{8}{9}M\right) = \frac{6000}{9}M = \frac{2000}{3}M

The number of women who claimed the gift is $\frac{2}{3}W$ , each receiving Rs 1000.
The total amount given to women is:

\text{Amount}_{\text{women}} = 1000 \times \left(\frac{2}{3}W\right) = \frac{2000}{3}W

Summing the two amounts:

\text{Total} = \frac{2000}{3}M + \frac{2000}{3}W = \frac{2000}{3}(M + W) = \frac{2000}{3} \times 300 = 2,00,000

Final answer

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2018 Computer Science and Information Technology (CS)
Question: 6 of 65, printed as GA Q.6
Section: General Aptitude

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