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# A Man walked from his house to office at 5kmph and got 20 mi

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Manager
Joined: 30 May 2013
Posts: 150
Location: India
Concentration: Entrepreneurship, General Management
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A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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24 Aug 2013, 22:06
2
1
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Difficulty:

55% (hard)

Question Stats:

72% (02:41) correct 28% (02:54) wrong based on 181 sessions

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A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km
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Joined: 24 Aug 2009
Posts: 445
Schools: Harvard, Columbia, Stern, Booth, LSB,
Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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24 Aug 2013, 22:22
4
1
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?
A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

Let the original distance and time be D & t
Case 1 - If man travels at 5kmph, he reaches late 20 min or 1/3 hr
We can write the same as
$$\frac{D}{5}$$ = t + $$\frac{1}{3}$$ -----(1)

Case 2 - If man travels at 7.5kmph, he reaches early 12 min or 1/5 hr
We can write the same as
$$\frac{D}{7.5}$$ = t - $$\frac{1}{5}$$ -----(2)

Solving both we get D = 8
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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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25 Aug 2013, 06:21
1
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

Discussed here: time-speed-and-distance-simplified-150163.html
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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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25 Aug 2013, 19:23
3
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

1 Distance traveled is the same in both the cases
2 5 * (t + 1/3) = 7.5 * (t- 1/5)
3 t=19/15 hrs
4 Substituting the value of t in the LHS of (2), Distance = 5 *( 19/15 +1/3) = 8 km

Substituting the value of t in RHS of (2) will also give the same answer
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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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11 Jan 2014, 08:17
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

I'm not sure if this method is valid but please comment

d/5 = t+20
d/7.5 = t-12

So 5t + 100 = 7.5t - 90

t = (190)(2)/5 = 78

So distance (78)(5) + 100 /60

C

I divided by 60 to go back to hours cause I was working with minutes before

Hope it helps
Cheers!
J
Manager
Joined: 07 Apr 2015
Posts: 153
A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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27 Aug 2015, 02:32
jlgdr wrote:

I'm not sure if this method is valid but please comment

d/5 = t+20
d/7.5 = t-12

So 5t + 100 = 7.5t - 90

t = (190)(2)/5 = 78

So distance (78)(5) + 100 /60

C

I divided by 60 to go back to hours cause I was working with minutes before

Hope it helps
Cheers!
J

I did it the same way, however t = (190*2)/5 should read = 76 not 78.

(76*5 + 100) / 60 = 8
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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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24 Nov 2016, 10:50
2
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

Distance is constant

$$\frac{5* ( t + 20 )}{60} = \frac{( t - 12 )*30}{4*60}$$

$$20( t + 20 ) = ( t - 12 )30$$

$$20t + 400 = 30t - 360$$

$$760 = 10t$$

So, $$t = 76$$

Thus distance = $$\frac{5( 76 + 20 )}{60}$$

Hence distace = 8 km

Answer will be (C) 8 Km

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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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24 Nov 2016, 13:48
rrsnathan wrote:
A Man walked from his house to office at 5kmph and got 20 minutes late. if he had travelled at 7.5kmph, he would have reached 12 minutes early. The distance from his house to office is?

A) 4Km
B) 16Km
C) 8Km
D) 9Km
E) 12Km

d/5-8/15=d/7.5
d=8 km
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Re: A Man walked from his house to office at 5kmph and got 20 mi  [#permalink]

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13 Jun 2019, 11:49
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Re: A Man walked from his house to office at 5kmph and got 20 mi   [#permalink] 13 Jun 2019, 11:49
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