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22 Jan 2026, 15:52
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
55%
(hard)
Question Stats:
70% (02:44) correct
30%
(03:00)
wrong
based on 141
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History
Date
Time
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Not Attempted Yet
Jayden and Anna walk from their aunt's house to a confectionery shop, which is at a distance of 27 miles, at 5 miles/hr and 7 miles/hr, respectively. Anna reaches the confectionery shop and immediately turns back, meeting Jayden on her way back in front of a dairy shop. What is the distance from their aunt's house to the dairy shop?
A. 22.5 miles
B. 20 miles
C. 18.5 miles
D. 15 miles
E. 13.5 miles
A. 22.5 miles
B. 20 miles
C. 18.5 miles
D. 15 miles
E. 13.5 miles
22 Jan 2026, 23:24
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First, let's calculate the time taken by Anna to reach the confectionary shop:
Time = 27/7 hours (as Time = Distance/Speed)
In the same time, Jayden covers a total of 5*(27/7) = 135/7 miles = 19.29 miles
At this point of time, the distance between the two of them = 27-(135/7) = 7.71 miles
As Anna turns back, now, they will be moving in the opposite directions, thus, their relative velocity = 12 miles/hour and the time taken to meet = 7.71/12 = 9/14 hours
Additional distance travelled by Jayden to reach the dairy shop = 5*(9/14) = 45/14 miles = 3.21 miles
Hence, the distance from their aunt's house to the dairy shop = 19.29 + 3.21 = 22.5 miles (Option A)
Time = 27/7 hours (as Time = Distance/Speed)
In the same time, Jayden covers a total of 5*(27/7) = 135/7 miles = 19.29 miles
At this point of time, the distance between the two of them = 27-(135/7) = 7.71 miles
As Anna turns back, now, they will be moving in the opposite directions, thus, their relative velocity = 12 miles/hour and the time taken to meet = 7.71/12 = 9/14 hours
Additional distance travelled by Jayden to reach the dairy shop = 5*(9/14) = 45/14 miles = 3.21 miles
Hence, the distance from their aunt's house to the dairy shop = 19.29 + 3.21 = 22.5 miles (Option A)
23 Jan 2026, 03:17
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I solved with approximation by eliminating options.
Since dairy shop is the meeting point of both Jayden and Anna, and distance between aunt's house to a confectionery shop is 27.
In next 4 hours Jayden will travel for 20 kms and Anna will travel 28 kms ( Anna has completed 27km and started returning back). And gap between Anna and Jayden is exactly 6 kms.
So the answer is definitely above 20kms that would be 22.5, since we have only one option A.
And to calculate exact number we can do that with relative speed, to cover 6 km it will take 6/(7+5) i.e. 6/12 = 0.5. So the total distance of dairy from house is 20 + 0.5 * 5 =22.5. Option A
Since dairy shop is the meeting point of both Jayden and Anna, and distance between aunt's house to a confectionery shop is 27.
In next 4 hours Jayden will travel for 20 kms and Anna will travel 28 kms ( Anna has completed 27km and started returning back). And gap between Anna and Jayden is exactly 6 kms.
So the answer is definitely above 20kms that would be 22.5, since we have only one option A.
And to calculate exact number we can do that with relative speed, to cover 6 km it will take 6/(7+5) i.e. 6/12 = 0.5. So the total distance of dairy from house is 20 + 0.5 * 5 =22.5. Option A
