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11 Jun 2025, 06:39
Kudos
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B
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
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A boy walks from his home to school at 5 kmph, reaches the school 4 minutes early. If he walks from his home to school at 4 kmph, he reaches the school 2 minutes late. Find the time taken by him to go to school if he walks at 6 kmph.
(A) 15 minutes
(B) 20 minutes
(C) 25 minutes
(D) 30 minutes
(A) 15 minutes
(B) 20 minutes
(C) 25 minutes
(D) 30 minutes
17 Jun 2025, 00:50
Kudos
Bookmarks
Given:
• The boy walks from home to school.
• If he walks at 5 kmph, he reaches 4 minutes early.
• If he walks at 4 kmph, he reaches 2 minutes late.
To find: The time (in minutes) he will take to reach school if he walks at 6 kmph.
Concept Clarification:
Let the required time to reach school on time (without being early or late) be T minutes.
Meaning:
• The boy starts at the right time to reach exactly on time in T minutes if he walks at the correct speed.
• If he walks faster at 5 kmph, he covers the distance quicker and arrives 4 minutes early, meaning he takes T – 4 minutes to reach.
• If he walks slower at 4 kmph, he takes T + 2 minutes to reach, so he arrives 2 minutes late.
Solution:
Let the distance from home to school be D km.
Then:
Since distance is the same in both cases, we have 15(T – 4) = 12(T + 2)
Correct Answer: (B)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
• The boy walks from home to school.
• If he walks at 5 kmph, he reaches 4 minutes early.
• If he walks at 4 kmph, he reaches 2 minutes late.
To find: The time (in minutes) he will take to reach school if he walks at 6 kmph.
Concept Clarification:
Let the required time to reach school on time (without being early or late) be T minutes.
Meaning:
• The boy starts at the right time to reach exactly on time in T minutes if he walks at the correct speed.
• If he walks faster at 5 kmph, he covers the distance quicker and arrives 4 minutes early, meaning he takes T – 4 minutes to reach.
• If he walks slower at 4 kmph, he takes T + 2 minutes to reach, so he arrives 2 minutes late.
Solution:
Let the distance from home to school be D km.
Then:
- At 5 kmph:
- Time = (T – 4)/60 hours
- Hence, D = 5 × (T – 4)/60 km
- D = (T – 4)/12
- At 4 kmph:
- Time = (T + 2)/60 hours
- Hence, D = 4 × (T + 2)/60
- D = (T + 2)/15
Since distance is the same in both cases, we have 15(T – 4) = 12(T + 2)
- 15T – 60 = 12T + 24
- 15T – 12T = 24 + 60
- 3T = 84
- T = 28 minutes
- So, D = 2 km (using any of the expressions for D)
- So, the scheduled time to reach school is 28 minutes.
- If he walks at 6 kmph, time taken = 2/6 hours
- = 1/3 hours = 20 minutes.
Correct Answer: (B)
Shweta Koshija
GMAT, GRE, SAT Coach for 10+ years
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