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Mathematics

Assertion (A) : If 3 pipes can fill a tank in 6 hours, then 6 pipes will fill the same tank in half the time.

Reason (R) : Time required to complete a certain work = Work to be completedOne day’s work\dfrac{\text{Work to be completed}}{\text{One day's work}}.

  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

If 3 pipes take 6 hours, then their combined rate of filling the tank is 16\dfrac{1}{6} tank/hr.

Each pipe's rate = 16×13\dfrac{1}{6} \times \dfrac{1}{3} = 118\dfrac{1}{18} tank/hr

Thus, 6 pipes will fill = 6 x 118=13\dfrac{1}{18} = \dfrac{1}{3} tank in an hr.

Time to fill 1 tank by 6 pipes = 3 hours

So, assertion (A) is true.

Time required to complete a certain work = Work to be completedOne day’s work\dfrac{\text{Work to be completed}}{\text{One day's work}}.

This is a standard formula used in time and work problems.

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

Hence, option 2 is the correct option.

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