Answer:
Given, total number of students = 1800 Number of students who opted basketball = 750 Number of students who opted cricket = 800 TIPS \[\therefore \] Number of students who opted table tennis = Total number of students - Number of students, who opted (basketball + cricket) \[=1800-(750+800)=1800-1550=250\] (a) Required ratio \[\text{=}\frac{\text{Number of students who opted basketball}}{\text{Number of students who opted table}\,\text{tennis}}\] \[=\frac{750}{250}=\frac{75}{25}\] [dividing numerator and denominator by 10] \[=\frac{75}{25}=\frac{75\div 25}{75\div 25}=\frac{3}{1}=3:1\] [\[\because \]HCF of 75 and 25 = 25] (b) Required ratio \[=\frac{\text{Number of students who opted cricket}}{\text{Number of students who opted basketball}}\] \[=\frac{800}{750}=\frac{80}{75}\] [dividing numerator and denominator by 10] \[=\frac{80\div 5}{75\div 5}=\frac{16}{15}=16:15\]\[\left[ \begin{align} & \because 80=2\times 2\times 5\times 2\times 2 \\ & \text{and}\,75=3\times 5\times 5 \\ & \therefore \,\text{HCF}\,\text{of}\,80\,\text{and}\,75=5 \\ \end{align} \right]\] (c) Required ratio \[=\frac{\text{Number of students who opted basketball}}{\text{Total number of students}}\] \[=\frac{750}{1800}=\frac{75}{180}\] [dividing numerator and denominator by 10] \[=\frac{75\div 15}{180\div 15}=\frac{5}{12}=5:12\] \[\left[ \begin{align} & \because \,75=3\times 5\times \,\text{and}\,180=3\times 5\times 3\times 2\times 2 \\ & \therefore \,\text{HCF}\,\text{of}\,75\,\text{and}\,180=3\times 5=15 \\ \end{align} \right]\]
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