CAT 2004QA Question 6

Basics of TSD/ProportinalityEasy

If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will arrive at the same place at 11 a.m. At what speed must he cycle to get there at noon?

Answer & solution

  • A

    11 km/hr

  • 12 km/hr

  • C

    13 km/hr

  • D

    14 km/hr

Solution

Let x hrs be the time required at 15kmph to reach the place at 11:00 am
∴ Distance that the man has to cycle = 15x km

Now, 15x10 = x + 2
​​​​​​​∴ 15x = 10x + 20
∴ 5x = 20
∴ x = 4 hrs

∴ Distance to be travelled = 60 km

∴ To reach the place at noon, the man should cycle for x + 1 = 5 hrs.

Let the new speed be y.

∴ 5 = 60y

∴ y = 12 km/hr

Hence, option (b).

CAT 2004 QA Q6: If a man cycles at 10 km/hr, then he arrives at a certain place at 1 p.m. If he cycles at 15 km/hr, he will ar — Solution | TheCATExam