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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late.

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Bunuel
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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink] New post   29 Jan 2021, 05:00
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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. Next day, she covers this distance at 12 km per hour and reaches the school 8minutes earlier than the scheduled time. What is the distance of her school from her house ?

(A) 15 km
(B) 20 km
(C) 22.5 km
(D) 25 km
(E) 26 km
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meanup
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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink] New post   29 Jan 2021, 05:08
Time Difference \(= 7-(-8)=15\) min

Distance \(= \frac{10*12}{(12-10)} *\frac{15}{60}=15\) Km

Ans A
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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink] New post   29 Jan 2021, 05:09
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Bunuel wrote:
Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. Next day, she covers this distance at 12 km per hour and reaches the school 8minutes earlier than the scheduled time. What is the distance of her school from her house ?

(A) 15 km
(B) 20 km
(C) 22.5 km
(D) 25 km
(E) 26 km


CONCEPT: Distance is constant in both journeys

DIstance = 10*(t+7) = 12*(t-8)

i.e 10t + 70 = 12t - 96

i.e. 2t = 166

i.e. t = 83 mins

Distance \(= 10*\frac{(83+7)}{60}\) (Now the time is in hours because speed is in km/hr)

ie. Distance = 15 km



ANswer: Option A
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Re: Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink] New post   29 Jan 2021, 05:11
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Let the correct time taken by Dimpy = t hours

By the law of proportions, when distance is constant s1 * t1 = s2 * t2

s1 = 10 km/h and t1 = (t + 7/60) (Converting minutes to hours)

s2 = 12 km/h and t2 = (t - 8/60)


Therefore 10 * (t + 7/60) = 12 * (t - 8/60)

10 t + (70/60) = 12t - (96/60)

166/60 = 2t

t = 83/60

Putting t in any of the equations will give us the distance.

10 * (83/60 + 7/60) = 10 * 90/60 = 15 km


Option A

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Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink] New post   11 Mar 2022, 02:01
meanup wrote:
Time Difference \(= 7-(-8)=15\) min

Distance \(= \frac{10*12}{(12-10)} *\frac{15}{60}=15\) Km

Ans A

meanup
Can you explain how did you reach at this part of the equation \frac{10*12}{(12-10)}
I did understood the concept behind this?
Thanks in advance
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gmatclubot
Dimpy goes to school at 10 km/h and reaches the school 7 minutes late. [#permalink]
11 Mar 2022, 02:01
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