Question : In a 1000 m race, Arjun, Balaji, and Charan are running. Arjun beats Balaji by 100 m, and Balaji beats Charan by 100 m. In the next 1000 m race (the speeds are the same as in the previous), Balaji gives Charan a head start of 100 m, and Arjun gives Balaji a head start of 100 m. Find the distance by which the winner is ahead of the person just behind him.
Option 1: 100 m
Option 2: 40 m
Option 3: 30 m
Option 4: 20 m
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: 20 m
Solution :
Let us denote Arjun by A, Balaji by B, and Charan by C. In a 1000 m race, Arjun beats Balaji by 100 m. Hence, while Arjun covers 1000 m, Bajali covers 900 m. So, $\small \text{Speed of Arjun}:\small \text{Speed of Balaji} = 1000 : 900 = 10 : 9 = 100 : 90$ In a 1000 m race, Balaji beats Charan by 100 m. Hence, while Balaji covers 1000 m, Charan covers 900 m. So, $\small \text{Speed of Balaji}: \small \text{Speed of Charan}= 1000 : 900 = 10 : 9 = 90 : 81$ Hence, $\small \text{Speed of Arjun} :\small \text{Speed of Balaji}: \small \text{Speed of Charan} = 100 : 90 : 81$ Let the speed of Arjun, Balaji, and Charan be $100s, 90s, \text{and}\ 81s$ respectively. In the next race, Arjun has to cover = 1000 m Balaji has to cover = 1000 – 100 = 900 cm Charan has to cover = 900 – 100 m = 800 m Also, Time taken by Arjun to reach the finish line = $\frac{1000}{100s} = \frac{10}{s}$ Time taken by Balaji to reach the finish line = $\frac{900}{90s} = \frac{10}{s}$ Time taken by Charan to reach the finish line = $\frac{800}{81s}$ It is visible that Charan will be the winner. By that time, Arjun will cover = $100s \times \frac{800}{81s} ≈ 980\ \text{m}$ Balaji will cover = $90s \times \frac{800}{81s} ≈ 880\ \text{m}$ Now, the distance by which the winner is ahead of the person just behind him = $1000 - 980 = 20\ \text{m}$ Hence, the correct answer is 20 m.
Candidates can download this ebook to know all about SSC CGL.
Answer Key | Eligibility | Application | Selection Process | Preparation Tips | Result | Admit Card
Question : In a 1200 m race, bike A beats bike B by 100 m. Bike B beats bike C by 100 m in a 600 m race. If bike A beats bike C by 30 sec in a 720 m race, then what is the speed of bike C?
Question : In a 1500 m race, X beats Y by 100 m and X beats Z by 240 m. By what distance does Y beat Z in the same race?
Question : In a 1500 m race, Anil beats Bakul by 150 m, and in the same race, Bakul beats Charles by 75 m. By what distance does Anil beat Charles?
Question : In a linear race of 1000 m, A beats B by 50 m or 5 seconds. What is the difference between the speeds (in m/s) of A and B?
Question : In a 200-metre linear race, if A gives B a start of 25 m, A wins the race by 10 seconds. Alternatively, if A gives B a start of 45 m, the race ends in a dead heat. How long does A take to run 200 m?
Regular exam updates, QnA, Predictors, College Applications & E-books now on your Mobile