Question: Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10 metres. To do a favour to Arjun, Karan starts 10 metres behind the starting line in a second 100-metre race. They both run at their earlier speeds. Which of the following is true in connection with the second race?

(A) Karan & Arjun reach finishing line together.
(B) Arjun beats Karan by 1 metre.
(C) Arjun beats Karan by 11 metres.
(D) Karan beats Arjun by 1 metre.
(E) Karan beats Arjun by 2 metre.

Correct Answer: D
Solution and Explanation:
Approach Solution 1:
Given:

Karan and Arjun run a 100 metres race, where Karan beats Arjun by 10 metres.
Karan starts 10 metres behind the starting line in a second 100 metre race. They both run at their earlier speeds.

Formula used:

Speed is directly proportional to the Distance

Calculation:

Karan and Arjun run a 100 metres race, where Karan beats Arjun by 10 metres.

When karan runs 100m and Arjun runs 90 m
⇒ Distance ratio = 100 : 90
⇒ Speed ratio = 100 : 90
⇒ 10 : 9

Karan starts 10 metres behind the starting line in a second 100 metre race.

Karan has runs 110 m

When Race is finish,
Arjun runs 9/10 of the karan runs
⇒ (9/10)× 110
⇒ 99 m Karan beats Arjun by 100 - 99
⇒ 1 m

Therefore, Karan beats Arjun by 1 m

Approach Solution 2:
In the 1st race when Karan runs 100 metres, Arjun runs only 90 metres.
Hence, the ratio of speeds of Arjun and Karan is 90 : 100 = 9 : 10
In the 2nd race, Karan has run 110 metres.
When he finishes the race, Arjun would have run 9/10×110= 99 metre
Therefore, Karan beats Arjun by 1 metre

Approach Solution 3:
^VK/^VA= 100/(100−10)= 10/9
Time taken to cover 110m by Karan= 110/10x= 11/x
Distance covered by Arjun in 11/x time= 9x*(11/x)= 99m
Karan beats Arjun by (100-99)= 1m

“Karan and Arjun run a 100-metre race, where Karan beats Arjun by 10”- is a topic of the GMAT Quantitative reasoning section of GMAT. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. GMAT Quant practice papers improve the mathematical knowledge of the candidates as it represents multiple sorts of quantitative problems.

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