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CAT 2020 Slot 3 — QA Question 11

Basics of TSD/ProportinalityEasy

Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 km/hr. She is late by 6 minutes if she drives at 35 km/hr. One day, she covers two-thirds of her distance to office in one-thirds of her usual time to reach office, and then stops for 8 minutes. The speed, in km/hr, at which she should drive the remaining distance to reach office exactly on time is

Answer & solution

  • A

    26

  • 28

  • C

    29

  • D

    27

Solution

Medium

First find the distance using the 66-minute difference between two speeds, then the usual time. Track the elapsed time after the fast first leg and the 88-minute halt, and apply speed == distance // time to the remaining stretch.

1

Find the distance dd. At 3535 km/hr she takes 66 min =660=\tfrac{6}{60} hr longer than at 4040 km/hr.

d35−d40=660⇒ d(40−3535×40)=110⇒ d⋅51400=110⇒ d=28 km\begin{aligned} &\frac{d}{35}-\frac{d}{40}=\frac{6}{60}\\ &\Rightarrow\ d\left(\frac{40-35}{35\times40}\right)=\frac{1}{10}\\ &\Rightarrow\ d\cdot\frac{5}{1400}=\frac{1}{10}\\ &\Rightarrow\ d=28\text{ km} \end{aligned}
2

Usual time. At her usual 4040 km/hr.

t=2840=0.7 hr⇒ t=42 min\begin{aligned} &t=\frac{28}{40}=0.7\text{ hr}\\ &\Rightarrow\ t=42\text{ min} \end{aligned}
3

Account for the fast leg and the halt. She covers 23\tfrac23 of the distance in 13\tfrac13 of the usual time, i.e. 13×42=14\tfrac13\times42=14 min, then halts 88 min.

Elapsed=14+8=22 min⇒ Time left=42−22=20 min\begin{aligned} &\text{Elapsed}=14+8=22\text{ min}\\ &\Rightarrow\ \text{Time left}=42-22=20\text{ min} \end{aligned}
4

Speed for the remaining 13\tfrac13 of distance. Remaining distance =13×28=283=\tfrac13\times28=\tfrac{28}{3} km in 2020 min =2060=\tfrac{20}{60} hr.

Speed=28/320/60=28/31/3⇒ Speed=28 km/hr\begin{aligned} &\text{Speed}=\frac{28/3}{20/60}=\frac{28/3}{1/3}\\ &\Rightarrow\ \text{Speed}=28\text{ km/hr} \end{aligned}
28 km/hr28\ \text{km/hr}
CAT 2020 Slot 3 QA Q11: Vimla starts for office every day at 9 am and reaches exactly on time if she drives at her usual speed of 40 k — Solution | TheCATExam