8th Class Mathematics Direct and Inverse Proportions

  • question_answer 5)                 A photograph of a bacteria enlarged 50,000 times attains a length of 5 cm as shown in the diagram. What is the actual length of the bacteria? If the photograph is enlarged 20,000 times only, what would be its enlarged length?

    Answer:

                    Actual length of the bacteria \[=\frac{5}{50000}\,cm\] \[=\frac{1}{10000}\,cm={{10}^{-4}}\,cm\] More the number of times a photograph of a bacteria is enlarged, more the length attained. So, the number of times a photograph of a bacteria is enlarged and the length attained are directly proportional to each other. So,          \[\frac{{{x}_{1}}}{{{y}_{1}}}=\frac{{{x}_{2}}}{{{y}_{2}}}\] \[\Rightarrow \]               \[\frac{50000}{5}=\frac{20000}{{{y}_{2}}}\] \[\Rightarrow \]               \[50000\,{{y}_{2}}=5\times 20000\] \[\Rightarrow \]               \[{{y}_{2}}=\frac{5\times 20000}{50000}\] \[\Rightarrow \]               \[{{y}_{2}}=2\] Hence, its enlarged length would be 2 cm.

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