Join WhatsApp Icon CAT WhatsApp Group
Question 18

On a 20 km tunnel, connecting two cities A and B, there are three gutters (1, 2 and 3). The distance between gutters 1 and 2 is half the distance between gutters 2 and 3. The distance from city A to its nearest gutter, gutter 1, is equal to the distance of city B from gutter 3. On a particular day, the hospital in city A receives information that an accident has happened at gutter 3. The victim can be saved only if an operation is started within 40 min. An ambulance started from city A at 30 km/hr and crossed gutter 1 after 5 min. If the driver had doubled the speed after that, what is the maximum amount of time would the doctor get to attend to the patient at the hospital. 

Assume that a total of 1 min is elapsed for taking the patient into and out of the ambulance?

Solution

Share

Let the distance between gutter 1 and A be x and between gutter 1 and 2 be y.

Hence, x + y + 2y + x = 20 => 2x+3y=20

Also x = 30kmph * 5/60 = 2.5km

Hence, y = 5km

After the ambulance doubles its speed it goes at 60kmph i.e. 1km per min. Hence, time taken for the rest of the journey = 15*2 + 2.5 = 32.5

It takes 1 min to load and unload the patient.

Hence, total time = 5 + 32.5 + 1 = 38.5 mins

So, the doctor would get 1.5 min to attend to the patient.

Was this solution helpful?

Get AI Help

Video Solution

video
View More Questions From Time, Speed and Distance

Create a FREE account and get:

  • All Quant CAT complete Formulas and shortcuts PDF
  • 41+ CAT previous year papers with video solutions PDF
  • 5000+ Topic-wise Previous year CAT Solved Questions for Free

CAT Quant Questions | CAT Quantitative Ability

CAT Probability, Combinatorics QuestionsCAT Profit and Loss QuestionsCAT Averages QuestionsCAT Coordinate Geometry QuestionsCAT Logarithms, Surds and Indices Questions

CAT DILR Questions | LRDI Questions For CAT

CAT Quant Based DI QuestionsCAT Miscellaneous LR QuestionsCAT Charts QuestionsCAT Maxima-Minima QuestionsCAT Selection With Condition Questions

CAT Verbal Ability Questions | VARC Questions For CAT

CAT Para Summary QuestionsCAT Odd One Out QuestionsCAT Reading Comprehension QuestionsCAT Critical Reasoning QuestionsCAT Verbal Ability Questions

Free CAT Quant Questions

CAT Time Speed DistanceCAT MensurationCAT Linear EquationsCAT PercentagesCAT Progressions and SeriesCAT LogarithmsCAT Coordinate GeometryCAT InequalitiesCAT Simple Interest Compound InterestCAT Probability, CombinatoricsCAT Venn DiagramsCAT Logarithms, Surds and IndicesCAT Functions, Graphs and StatisticsCAT RemaindersCAT Number SystemsCAT AveragesCAT ArithmeticCAT Time And WorkCAT Profit and LossCAT Profit And LossCAT Time, Speed and DistanceCAT Number SeriesCAT AlgebraCAT Quadratic EquationsCAT Averages, Ratio and ProportionCAT Data SufficiencyCAT MiscellaneousCAT GeometryCAT Averages Mixtures Alligations

Related Formulas With Tests

Speed - Distance - Time m/s to km/hr conversion.

Book Free CAT Mentorship

Get personalized CAT strategy from a 99%iler

500+ students mentored
CAT mentor

Join CAT 2026 course by 5-Time CAT 100%iler

Start your IIM journey with the right preparation and crack CAT 2026.

Enroll Now
Ask AI