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(C) Let $p$ be the number of persons who speak both languages.Given:$\alpha + p = 75$ (Only English)$\beta + p = 40$ (Only Hindi)$\alpha + \beta + p =

Vedclass · Accepted Answer

$\frac{\sqrt{119}}{12}$

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(C) Let $p$ be the number of persons who speak both languages.Given:$\alpha + p = 75$ (Only English)$\beta + p = 40$ (Only Hindi)$\alpha + \beta + p = 100$ (Total persons)Adding the first two equations: $\alpha + \beta + 2p = 115$.Subtracting the third equation: $p = 115 - 100 = 15$.Then,$\alpha = 75 - 15 = 60$ and $\beta = 40 - 15 = 25$.The equation of the ellipse is $25(\beta^2 x^2 + \alpha^2 y^2) = \alpha^2 \beta^2$.Dividing by $25 \alpha^2 \beta^2$: $\frac{x^2}{\alpha^2} + \frac{y^2}{\beta^2} = \frac{1}{25}$.This is $\frac{x^2}{(\alpha/5)^2} + \frac{y^2}{(\beta/5)^2} = 1$.Here,$a = \frac{60}{5} = 12$ and $b = \frac{25}{5} = 5$.Since $a > b$,the eccentricity $e = \sqrt{1 - \frac{b^2}{a^2}} = \sqrt{1 - \frac{25}{144}} = \sqrt{\frac{119}{144}} = \frac{\sqrt{119}}{12}$.

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