Question

In covering a distance of 30 km, Abhay takes 2 hours more than Sameer. If Abhay doubles his speed, then he would take 1 hour less than Sameer. Abhay's speed is:

• A. 5 kmph
• B. 6 kmph
• C. 6.25 kmph
• D. 7.5 kmph

Answer 1

The Correct Option is A

To find Abhay's speed, we need to set up equations based on the information given. Let's define:

Let \( A \) be Abhay's speed in kmph.

Let \( S \) be Sameer's speed in kmph. 

1. Equation from the first condition: In covering 30 km, Abhay takes 2 hours more than Sameer.
   1. The time taken by Sameer to cover 30 km = \( \frac{30}{S} \)
   2. The time taken by Abhay to cover 30 km = \( \frac{30}{A} \)
   3. According to the condition: \(\frac{30}{A} = \frac{30}{S} + 2\)
2. Equation from the second condition: If Abhay doubles his speed, he takes 1 hour less than Sameer.
   1. If Abhay doubles his speed, his new speed = \( 2A \)
   2. Time taken by Abhay when he doubles his speed = \(\frac{30}{2A}\)
   3. According to the condition: \(\frac{30}{2A} = \frac{30}{S} - 1\)

Now we have two equations:

• \(\frac{30}{A} = \frac{30}{S} + 2 \) (Equation 1)
• \(\frac{30}{2A} = \frac{30}{S} - 1 \) (Equation 2)

We can solve these equations to find the value of \( A \).

1. From Equation 1: \(\frac{30}{A} = \frac{30}{S} + 2\)
2. Rewrite as: \(\frac{30}{A} - \frac{30}{S} = 2\)
3. Let: \( \frac{30}{A} - \frac{30}{S} = 2 \) can be rewritten as:
4. \( 30 \left(\frac{S-A}{AS}\right) = 2\)
5. Simplify: \( 15(S-A) = AS \)
6. From Equation 2: \(\frac{30}{2A} = \frac{30}{S} - 1\)
7. Rewrite as: \(\frac{30}{S} - \frac{15}{A} = 1\)
8. Re-arrange: \( 30 - \frac{15S}{A} = S\)
9. Both equations result in the value finding for \( A \) as 5 kmph.

By solving the above relations, we can verify that when \( A = 5 \), both equations are satisfied. Therefore, Abhay's speed is 5 kmph.