CAT 2022 Set-2 | Quantitative Aptitude | Question: 15

Question

Two ships meet mid-ocean, and then, one ship goes south and the other ship goes west, both travelling at constant speeds. Two hours later, they are $60 \mathrm{~km}$ apart. If the speed of one of the ships is $6 \mathrm{~km}$ per hour more than the other one, then the speed, in km per hour, of the slower ship is

• A. $24$
• B. $18$
• C. $20$
• D. $12$

   

Comments

Let the speed of slower ship be x kmph

So the speed of faster ship will be (x+6)kmph

Distance covered by them in 2hr will be

Slower ship=2x   Faster ship=2(x+6)=2x+12 Both ships are 60km apart

Using pythagoras theorem, 60^2=(2x)^2+(2x+12)^2

                                            3600=8x^2+48x+144

                                            x^2+6x-432=0

                                            x^2+24x-18x-432=0
                                            x=18,-24 speed can not be negative so x=18

   Hence the speed of the slower ship will be 18kmph.So option b is the correct answer