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Mathematics

The values of a and b from the table are:

xy
318
5a
b90
848
  1. a = 30 and b = 270

  2. a = 30 and b = 15

  3. a = 45 and b = 15

  4. a = 30 and b = 540

Direct & Inverse Variations

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Answer

318=16\dfrac{3}{18} = \dfrac{1}{6}

848=16\dfrac{8}{48} = \dfrac{1}{6}

So, we can say that x and y vary directly

318=5a=b90=848318=5a and 318=b90a=5×185 and b=3×9018a=903 and b=27018a=30 and b=15\therefore \dfrac{3}{18} = \dfrac{5}{a} = \dfrac{b}{90} = \dfrac{8}{48}\\[1em] \Rightarrow \dfrac{3}{18} = \dfrac{5}{a} \text{ and } \dfrac{3}{18} = \dfrac{b}{90}\\[1em] \Rightarrow a = \dfrac{5 \times 18}{5} \text{ and } b = \dfrac{3 \times 90}{18}\\[1em] \Rightarrow a = \dfrac{90}{3} \text{ and } b = \dfrac{270}{18}\\[1em] \Rightarrow a = 30 \text{ and } b = 15

Hence, option 2 is the correct option.

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