6th Class Mathematics Ratio and Propotion

  • question_answer 18) Write true (T) or false (F) against each of the following statements: (a) 16 : 24 : : 20 : 30          (b) 21: 6 : : 35 : 10             (c) 12 : 18 : : 28 : 12        (d) 8 : 9 : : 24 : 27 (e) 5.2 : 3.9 : : 3 : 4            (f) 0.9 : 0.36 : : 10 : 4 TIPS Firstly, write the given ratios in lowest form. If lowest form of both ratios   are same, then they will be in proportion and given statement will be true, otherwise given statement will be false,                     

    Answer:

                    (a) We have, 16 : 24 : : 20 : 30 \[\therefore \]Ratio of 16 to \[24=\frac{16}{24}=\frac{16\div 8}{24\div 8}=\frac{2}{3}=2:3\] [\[\because \]HCF of 16 and \[24=2\times 2\times 2=8\]] and ratio of 20 to \[30=\frac{20}{30}=\frac{20\div 10}{30\div 10}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 10] Here, 16 : 24 = 20 : 30 = 2 : 3, so 16 : 24 :: 20 : 30 Hence, given statement is true. (b) We have, 21 : 6 : : 35 : 10 Ratio of 21 to \[6=\frac{21}{6}=\frac{21\div 3}{6\div 3}=\frac{7}{2}=7:2\] [dividing numerator and denominator both by 3] and ratio of 35 to \[10=\frac{35}{10}=\frac{35\div 5}{10\div 5}=\frac{7}{2}=7:2\] [dividing numerator and denominator both by 5] Here, 21 : 6 = 35 : 10 = 7 : 2, so 21 : 6 : : 35 : 10 Hence, given statement is true. (c) We have, 12 : 18 : : 28 : 12 \[\therefore \] Ratio of 12 to\[18=\frac{12}{18}=\frac{12\div 6}{18\div 6}=\frac{2}{3}=2:3\] [dividing numerator and denominator both by 6] and ratio of 28 to \[12=\frac{28}{12}=\frac{28\div 4}{12\div 4}=\frac{7}{3}=7:3\] [dividing numerator and denominator both by 4] Here, \[2:3\ne 7:3\]i.e.\[12:18\ne 28:12\] Hence, given statement is false. (d) We have, 8 : 9 : : 24 : 27 Ratio of 8 to \[9=\frac{8}{9}=8:9\] and ratio of 24 to \[27=\frac{24}{27}=\frac{24\div 3}{27\div 3}=\frac{8}{9}=8:9\] [dividing numerator and denominator both by 3] Here, 8 : 9 = 24 : 27, so 8 : 9 : : 24 : 27 Hence, given statement is true. (e) We have, 5.2 : 3.9 : : 3 : 4 Ratio of 5.2 to \[3.9=\frac{5.2}{3.9}=\frac{52}{39}\] [multiplying numerator and denominator both by 10] \[=\frac{52\div 13}{39\div 13}=\frac{4}{3}=4:3\] [\[\because \]HCF of 52 and 39 = 13] and ratio of 3 to \[4=\frac{3}{4}=3:4\] Here, \[4:3\ne 3:4\,\text{i}\text{.e}\text{.}\,5.2:3.9\ne 3:4\] Hence, given statement is false. (f) We have, 0.9 : 0.36 : : 10 : 4 \[\therefore \]Ratio of 0.9 to \[0.36=\frac{0.9}{0.36}=\frac{90}{36}\] [multiplying numerator and denominator both by 100] \[=\frac{90\div 18}{36\div 18}=\frac{5}{2}=5:2\] [\[\because \]HCF of 36 and \[90=2\times 3\times 3=18\]] and ratio of 10 to \[4=\frac{10}{4}=\frac{10\div 2}{4\div 2}=\frac{5}{2}=5:2\] [dividing numerator and denominator both by 2] Here, \[0.9:0.36=10:4=5:2,\]so\[0.9:0.36::10:4\] Hence, given statement is true.

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