question_answer 11)

Out of 1800 students in a school, 750 opted basketball 800 opted cricket and remaining opted table tennis. If a student can opted only one game, find the ratio of (a) number of students, who opted basketball to the number of students who opted table tennis. (b) number of students, who opted cricket to the number of students opting basketball. (c) number of students, who opted basketball to the total number of students.

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] \[=\frac{75\div 15}{180\div 15}=\frac{5}{12}=5:12\] \[\left[ \begin{align}   & \because \,75=3\times 5\times \,\text{and}\,180=3\times 5\times 3\times 2\times 2 \\  & \therefore \,\text{HCF}\,\text{of}\,75\,\text{and}\,180=3\times 5=15 \\ \end{align} \right]\]