Question: Two cyclists start from the same place to ride in the same direction. A starts at noon at 8 kmph while B starts at 2 pm at the rate of 10 kmph. How far will A have ridden before he is overtaken by B?
- 75 km
- 76 km
- 78 km
- 80 km
- 84 km
“Two cyclists start from the same place to ride in the same direction.”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Prep Plus”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Solution and Explanation:
Approach Solution 1:
Let the time taken by A be = t hours
Time taken by B = t−2 hours
When A meets B, Distance travelled by both is the same.
--> DA = DB
--> 8∗t = 10∗(t−2)
--> 8t = 10t−20
--> 2t = 20
--> t = 10 hours
Distance travelled by A, DA = 8∗10
= 80 kms
Correct Answer: D
Approach Solution 2:
Given
- Two cyclists start from the same place to ride in the same direction.
- A starts at noon at 8 kmph while B starts at 2 pm at the rate of 10 kmph
To find
We need to determine
- The distance A has travelled before he is overtaken by B
Approach and Working out
When B starts journey, A has already travelled for 2 hours, and a distance of 8 x 2 = 16 km
- Hence, from 2 pm, the time taken by B to catch A = 16/10–8 hrs = 8 hrs
Therefore, A travels a total of 2 + 8 = 10 hours before B catches and overtakes A
- So, total distance travelled by A till that time = 10 x 8 = 80 km
Correct Answer: D
Approach Solution 3:
At 2 PM, A has been travelling for 2 hours; thus, A is 2 * 8 = 16 km from the starting point.
Since B is 10 - 8 = 2 km/h faster than A, it will take B 16/2 = 8 hours to catch up with A. So, B will overtake A at 2 PM + 8 hours = 10 PM.
At 10 PM, A has been travelling for 10 hours; thus, A will have travelled 8 x 10 = 80 km before being overtaken.
Correct Answer: D
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