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?

1. 75 km
2. 76 km
3. 78 km
4. 80 km
5. 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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