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Question Number 186675 by pascal889 last updated on 08/Feb/23

Answered by ARUNG_Brandon_MBU last updated on 08/Feb/23

∗The ratio of girls to boys is 5:6 ⇒ (G/B)=(5/6) ⇒G=(5/6)B ...eqn(i) ∗On a rainy day: (1/6)G were absent ⇒(5/6)G were present. (1/4)B were absent ⇒(3/4)B were present. ∗ The number of pupil present that day was 390 ⇒(5/6)G+(3/4)B=390 ...eqn(ii) Substituting eqn(i) in eqn(ii) ⇒(5/6)×(5/6)B+(3/4)B=390 ⇒((13)/9)B=390 ⇒B=270 and G=(5/6)×270=225 270 pupil out of 495 are boys//

$$\ast\mathrm{The}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{girls}\:\mathrm{to}\:\mathrm{boys}\:\mathrm{is}\:\mathrm{5}:\mathrm{6} \\ $$$$\Rightarrow\:\frac{{G}}{{B}}=\frac{\mathrm{5}}{\mathrm{6}}\:\Rightarrow{G}=\frac{\mathrm{5}}{\mathrm{6}}{B}\:...\mathrm{eqn}\left({i}\right) \\ $$$$\ast\mathrm{On}\:\mathrm{a}\:\mathrm{rainy}\:\mathrm{day}: \\ $$$$\:\frac{\mathrm{1}}{\mathrm{6}}{G}\:\mathrm{were}\:\mathrm{absent}\:\Rightarrow\frac{\mathrm{5}}{\mathrm{6}}{G}\:\mathrm{were}\:\mathrm{present}. \\ $$$$\frac{\mathrm{1}}{\mathrm{4}}{B}\:\mathrm{were}\:\mathrm{absent}\:\Rightarrow\frac{\mathrm{3}}{\mathrm{4}}{B}\:\mathrm{were}\:\mathrm{present}. \\ $$$$\ast\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pupil}\:\mathrm{present}\:\mathrm{that}\:\mathrm{day}\:\mathrm{was}\:\mathrm{390} \\ $$$$\Rightarrow\frac{\mathrm{5}}{\mathrm{6}}{G}+\frac{\mathrm{3}}{\mathrm{4}}{B}=\mathrm{390}\:...\mathrm{eqn}\left({ii}\right) \\ $$$$\mathrm{Substituting}\:\mathrm{eqn}\left({i}\right)\:\mathrm{in}\:\mathrm{eqn}\left({ii}\right)\: \\ $$$$\Rightarrow\frac{\mathrm{5}}{\mathrm{6}}×\frac{\mathrm{5}}{\mathrm{6}}{B}+\frac{\mathrm{3}}{\mathrm{4}}{B}=\mathrm{390}\:\Rightarrow\frac{\mathrm{13}}{\mathrm{9}}{B}=\mathrm{390} \\ $$$$\Rightarrow{B}=\mathrm{270}\:\mathrm{and}\:{G}=\frac{\mathrm{5}}{\mathrm{6}}×\mathrm{270}=\mathrm{225} \\ $$$$\mathrm{270}\:\mathrm{pupil}\:\mathrm{out}\:\mathrm{of}\:\mathrm{495}\:\mathrm{are}\:\mathrm{boys}// \\ $$

Answered by Rasheed.Sindhi last updated on 08/Feb/23

determinant (( ,G,B,(Total)),( ,(5x),(6x),(11x)),((Absents on_(the rainy day) ),(5x/6),(6x/4),(7x/3)),((Presents on_(the rainy day) ), , ,((26x)/3))) ((26x)/3)=390⇒x=((390×3)/(26))=45 Boys: 6x=6×45=270

$$\begin{array}{|c|c|c|c|}{\:}&\hline{{G}}&\hline{{B}}&\hline{{Total}}\\{\:}&\hline{\mathrm{5}{x}}&\hline{\mathrm{6}{x}}&\hline{\mathrm{11}{x}}\\{\underset{{the}\:{rainy}\:{day}} {{Absents}\:{on}}\:}&\hline{\mathrm{5}{x}/\mathrm{6}}&\hline{\mathrm{6}{x}/\mathrm{4}}&\hline{\mathrm{7}{x}/\mathrm{3}}\\{\underset{{the}\:{rainy}\:{day}} {{Presents}\:{on}}}&\hline{\:}&\hline{\:}&\hline{\frac{\mathrm{26}{x}}{\mathrm{3}}}\\\hline\end{array} \\ $$$$\frac{\mathrm{26}{x}}{\mathrm{3}}=\mathrm{390}\Rightarrow{x}=\frac{\mathrm{390}×\mathrm{3}}{\mathrm{26}}=\mathrm{45} \\ $$$${Boys}:\:\mathrm{6}{x}=\mathrm{6}×\mathrm{45}=\mathrm{270} \\ $$$$ \\ $$

Commented by Ar Brandon last updated on 08/Feb/23

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Commented by Rasheed.Sindhi last updated on 08/Feb/23

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