CAT Quantitative Aptitude Questions | CAT Time Speed and Distance & Races

The question is from the topic time and distance. Speed is decreaed due to an accident and it takes extra time, what could be the distance and actual speed. Time Speed and Distance is a favorite in CAT Exam, and appears more often than expected in the CAT Quantitative Aptitude section in the CAT Exam

Question 23 : Raj was travelling to his hometown from Mumbai. He met with a small accident 80 Km away from Mumbai and continued the remaining journey at 4/5 of his original speed and reached his hometown 1 hour and 24 minutes late. If he had met with the accident 40 Km further, he would have been an hour late. i) What is Raj's normal speed?
A) 20 Km/hr B) 15 Km/hr C) 30 Km/hr D) 25 Km/hr
ii) What is the distance between Mumbai and Raj's hometown?
A) 140 Km B) 200 Km C) 220 Km D) 250 Km

Explanatory Answer

Method of solving this CAT Question from Time Speed Distance: Create a visual for the route he travels

Scenario 1:

\\frac{5D1}{4s}\\) − \\frac{D1}{s}\\) = 1 + \\frac{24}{60}\\) (always write minutes in this form if the unit is Km/hr)
=> \\frac{D1}{s}\\) = \\frac{7}{5}\\) * 4 = \\frac{28}{5}\\) hours

Scenario 2:

\\frac{5D2}{4s}\\) − \\frac{D2}{s}\\) = 1
=> \\frac{D2}{s}\\) = 4 hours
i) Therefore, in his normal speed, he can travel 40 Km in \\frac{28}{5}\\) - 4 = \\frac{8}{5}\\) hours so,
s = \\frac{40}{8/5}\\) = 25 Km/hr.
ii) \\frac{D1}{s}\\) = \\frac{28}{5}\\) => D1 = 140 Km. Therefore, total distance D = 140 + 80 = 220 Km.

The question is "i) What is Raj's normal speed? and ii) What is the distance between Mumbai and Raj's hometown? "

Hence, the answer is 25 Km/hr and 220 Km.

Choice i) D & ii) C is the correct answer.