Question : X and Y travel a distance of 90 km each such that the speed of Y is greater than that of X. The sum of their speeds is 100 km/hr and the total time taken by both is 3 hours 45 minutes. The ratio of the speed of X to that of Y is:
Option 1: 2 : 3
Option 2: 1 : 3
Option 3: 2 : 4
Option 4: 1 : 4
Latest: SSC CGL preparation tips to crack the exam
Don't Miss: SSC CGL complete guide
New: Unlock 10% OFF on PTE Academic. Use Code: 'C360SPL10'
Correct Answer: 2 : 3
Solution : Let the speed of Y be $a$ ⇒ Speed of X = $100 - a$ Time = 3 hours 45 minutes = $\frac{15}{4}$ hours According to the question, $\frac{90}{a} + \frac{90}{100 - a} = \frac{15}{4}$ ⇒ $\frac{9000 - 90a + 90a}{100a - a^2}= \frac{15}{4}$ ⇒ $36000 = 1500a - 15a^2=0$ ⇒ $15a^2 - 1500a + 36000 = 0$ ⇒ $a^2 - 100a + 2400 = 0$ ⇒ $a^2 - 60a - 40a + 2400 = 0$ ⇒ $a(a - 60) - 40(a - 60) = 0$ ⇒ $(a - 60) (a - 40) = 0$ ⇒ $a = 60, 40$ As Y is faster than X So, Y = 60 km/hr And X = 40 km/hr So, the required ratio = 40 : 60 = 2 : 3 Hence, the correct answer is 2 : 3.
Candidates can download this ebook to know all about SSC CGL.
Admit Card | Eligibility | Application | Selection Process | Preparation Tips | Result | Answer Key
Question : Two trains, A and B, start from stations X and Y and travel towards Y and X, respectively. After passing each other, they take 4 hours 48 minutes, and 3 hours 20 minutes respectively to reach Y and X. If train A is moving at 45 km/hr, then the speed of train B is:
Question : A is faster than B. A and B each walk 24 km. The sum of their speeds is 7 km/hr and the sum of their time taken is 14 hours. Then A's speed is equal to:
Question : If the speed of a boat in still water is 20 km/hr and the speed of the current is 5 km/hr, then the time taken by the boat to travel 100 km with the current is:
Question : A thief running at a speed of ‘$x$’ km/hr is chased by a policeman running at a speed of 10 km/hr. If the thief is ahead by 100 metres, the policeman catches the thief after 3 minutes. At what speed is the thief running (‘$x$’ being the unknown
Question : Rameshwar goes on a trip on his motorcycle and rides for 405 kilometres. If he rides for 6 hours at a speed of 45 km/hr, find at what speed he travels for the remaining 3 hours of the journey.
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile