Multiple choice

The questions given below contain two statements giving certain data. You have to decide whether the data given in the statements are sufficient for answering the question. What is the difference between present ages of Shashi and Ranu ? (i) The ratio of the present age of Ranu to that of Shashi six years ago is 4 : 1. (ii) The ratio of the present age of Shashi and Ranu is 2 : 5.

  1. If statement I alone is sufficient but statement II alone is not sufficient.

  2. If statement II alone is sufficient but statement I alone is not sufficient.

  3. If each statement alone (either I or II) is sufficient.

  4. If statement I and II together are not sufficient.

  5. If both statement together are sufficient, but neither statement alone is sufficient.
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E Correct answer
Explanation

Statement I gives ratio of Ranu's present age to Shashi's age six years ago as 4:1, which is insufficient alone as we have one equation with two unknowns. Statement II gives present age ratio of Shashi:Ranu as 2:5, also insufficient alone. Together, let Shashi's present age = 2x, Ranu's present age = 5x. From I: 5x/(2x-6) = 4/1. Solving: 5x = 8x-24, so 3x = 24, x = 8. Shashi = 16, Ranu = 40. Difference = 24. Both statements together are necessary and sufficient.

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