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Mathematics

Assertion (A) : The cost of 16 bulbs is ₹ 144. The number of bulbs than can be bought for ₹ 270 is 30.

Reason (R) : In inverse variation, the ratio of one kind of like terms is equal to the inverse ratio of the second kind of like terms.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Direct & Inverse Variations

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Answer

Given,

The cost of 16 bulbs = ₹ 144

The cost of 1 bulb = 14416\dfrac{144}{16} = ₹ 9

Number of bulbs for ₹ 270 = Total moneyPrice of each bulb=2709\dfrac{\text{Total money}}{\text{Price of each bulb}} = \dfrac{270}{9} = 30

So, assertion (A) is true.

In inverse variation,

x1y1=x2y2x1x2=y2y1\Rightarrow x1y1 = x2y2\\[1em] \Rightarrow \dfrac{x1}{x2} = \dfrac{y2}{y1}\\[1em]

So, reason (R) is true but, reason (R) does not explains assertion(A).

Hence, option 2 is the correct option.

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