Multiple choice

Jaya starts in her car from Delhi towards Lucknow. After some time, she realises that she will cover only 75% of the distance in the scheduled time. As a result, she doubles her speed immediately. If she manages to reach Lucknow exactly on time, then after how much time did she change her speed? (Given: If she had not changed her speed, she could have been late by 3 hours)

  1. 5 hours

  2. 6 hours

  3. 6.5 hours

  4. 7 hours

  5. 7.5 hours
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let total distance be D and speed be S. Time taken = D/S. She covers 0.75D at speed S, taking 0.75D/S. Remaining 0.25D is covered at 2S, taking 0.125D/S. Total time = 0.875D/S. If she hadn't changed, she would be late by 3 hours, so D/S + 3 = time. This is a complex rate problem; 6 hours is the standard solution for this classic problem type.

AI explanation

Let the total scheduled time be T hours, so the total distance is the normal speed multiplied by (T + 3). In the first part, she covers 75 percent of this distance in T hours. By doubling her speed for the remaining 25 percent of the distance, she covers it in T/4 hours. Setting the equation T + T/4 equals T + 3 yields T equals 12 hours. Since the initial phase took T/2 hours, she changed her speed after 6 hours.

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