question_answer 6)

Find the ratio of the following. (a) 81 to 108                       (b) 98 to 63 (c) 33 km to 121 km        (d) 30 min to 45 min

Answer:

                (a) Required ratio \[=\frac{81}{108}\] \[\because \] \[81=3\times 3\times 3\times 3\] and \[108=3\times 3\times 3\times 2\times 2\] HCF of 81 and 108 = 27 Ratio \[=\frac{81\div 27}{108\div 27}=\frac{3}{4}=3:4\] (b) Required ratio \[=\frac{98}{63}\] \[\therefore \]\[98=2\times 7\times 7\] and \[63=3\times 3\times 7\] \[\therefore \] HCF of 98 and 63 = 7 Ratio\[=\frac{98\div 7}{63\div 7}=\frac{14}{9}=14:9\] (c) Required ratio \[=\frac{33km}{121km}=\frac{33}{121}\] \[\therefore \] \[33=3\times 11\] and \[121=11\times 11\] \[\therefore \] HCF of 33 and 121 = 11 Ratio \[=\frac{33\div 11}{121\div 11}=\frac{3}{11}=3:11\] (d) Required ratio \[=\frac{30\min }{45\min }=\frac{30}{45}\] \[\therefore \] \[45=3\times 5\times 3\] and \[30=3\times 5\times 2\] \[\therefore \] HCF of 30 and 45 = 15 Ratio \[=\frac{30\div 15}{45\div 15}=\frac{2}{3}=2:3\]