Multiple choice

Points A and B are both in the line segment PQ and on the same side of its midpoint. A divides PQ in the ratio 2:3, and B divides PQ in the ratio 3:4. If AB = 2, then the length of PQ is-

  1. 70

  2. 75

  3. 80

  4. 85

  5. None of these
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A Correct answer
Explanation

Let PQ = x. Point A divides PQ in ratio 2:3, so A is at (2/5)x from P. Point B divides PQ in ratio 3:4, so B is at (3/7)x from P. Since both are on the same side of the midpoint, the distance AB = (3/7)x - (2/5)x = (15/35 - 14/35)x = (1/35)x. Given AB = 2, we have (1/35)x = 2, so x = 70. Therefore, PQ = 70.

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