CAT 2024 Slot 3 QA Q15 Time, Speed & Distance

Question 15 of the Quantitative Ability (QA) section, CAT 2024 Slot 3, with CAT's official answer and a worked solution.

A train travelled a certain distance at a uniform speed. Had the speed been 6 km per hour more, it would have needed 4 hours less. Had the speed been 6 km per hour less, it would have needed 6 hours more. The distance, in km, travelled by the train is
  1. A
    780
  2. B
    720
  3. C
    640
  4. D
    800

Answer: (B) 720 Time, Speed & Distance MCQ

Solution

  1. \(\frac{d}{v} - \frac{d}{v+6} = 4 \Rightarrow \frac{6d}{v(v+6)} = 4\), and \(\frac{d}{v-6} - \frac{d}{v} = 6 \Rightarrow \frac{6d}{v(v-6)} = 6\).
  2. Dividing: \(\frac{v-6}{v+6} = \frac{2}{3} \Rightarrow v = 30\).
  3. \(d = \frac{4 \times 30 \times 36}{6} = 720\) km.

Same concept in other years

See every question on Late at one speed, early at another: solve for distance.

More Time, Speed & Distance questions from CAT

All 48 Time, Speed & Distance questions asked since 2017.