Difficult Rate sum

Expert replies

[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed Jun 08, 2011 3:08 am

A man traveled a distance of 80 km in 7 hrs partly on foot at the rate of 8 km. per hour and partly on bicycle at 16km. per hour. Find the distance traveled on food.

A] 36
B]42
C]32
D] 56
E] 28

OA later,,,

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cans: Legendary Member; Posts: 1309; Joined: Mon Apr 04, 2011 5:34 amFollowed by: 123 members; Location: India; Thanked: 310 times; GMAT Score:750

by cans » Wed Jun 08, 2011 3:15 am

let x be distance traveled on foot. thus 80-x on bicycle
Time taken by foot distance = x/8
time taken by bicycle distance = (80-x)/16 = 5 - x/16
total time = x/8 + 5 - x/16 = 7
x/16 = 2
x=32
IMO C

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manpsingh87: Master | Next Rank: 500 Posts; Posts: 436; Joined: Tue Feb 08, 2011 3:07 amFollowed by: 6 members; Thanked: 72 times

by manpsingh87 » Wed Jun 08, 2011 3:37 am

[email protected] wrote:A man traveled a distance of 80 km in 7 hrs partly on foot at the rate of 8 km. per hour and partly on bicycle at 16km. per hour. Find the distance traveled on food.

A] 36
B]42
C]32
D] 56
E] 28

OA later,,,

let p be the no. of hours for which a man traveled on foot and q be the no. of hours for which man traveled on bicycle.

so distance traveled on foot=8p;
also 8p+16q=80;----1)
and p+q=7;----2)
multiply 2 with 16 we have;
16p+16q=112;
now subtract 1 from the above equation we have
8p=32;
hence c[spoiler][/spoiler]

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khound.siddharth: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Thu May 19, 2011 8:44 am; Thanked: 1 times

by khound.siddharth » Wed Jun 08, 2011 5:17 am

Such questions are best ans by taking the options and working with them to get the soln.
Start with the middle value and then work out. If the tried value is less than go for the nxt higher figure...if low then take the next lower value.
Here if I start with option c for instance -
32 kmps / 8 = 4 hts
remaining kms -> 48/16 = 3 hrs
4+3 = 7 hrs...just what the question said - the person coverd 80 kms in 7 hrs.

My 2 cents.

khound.siddharth: Junior | Next Rank: 30 Posts; Posts: 12; Joined: Thu May 19, 2011 8:44 am; Thanked: 1 times

by khound.siddharth » Wed Jun 08, 2011 5:19 am

[email protected]: Legendary Member; Posts: 934; Joined: Tue Nov 09, 2010 5:16 amFollowed by: 14 members; Location: AAMCHI MUMBAI LOCAL; Thanked: 63 times

by [email protected] » Wed Jun 08, 2011 6:12 am

Thank you guyz for helping me. It was not difficult but rather chicky....

iamsaurav: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Sun Sep 05, 2010 8:58 pm; GMAT Score:710

by iamsaurav » Wed Jun 08, 2011 7:24 am

khound.siddharth wrote:Such questions are best ans by taking the options and working with them to get the soln.
Start with the middle value and then work out. If the tried value is less than go for the nxt higher figure...if low then take the next lower value.
Here if I start with option c for instance -
32 kmps / 8 = 4 hts
remaining kms -> 48/16 = 3 hrs
4+3 = 7 hrs...just what the question said - the person coverd 80 kms in 7 hrs.

My 2 cents.

finites: Junior | Next Rank: 30 Posts; Posts: 26; Joined: Thu Jun 02, 2011 7:21 am

by finites » Wed Jun 08, 2011 11:55 am

16x + 8y = 80

x + y =7

x + x + y = 10

x + 7 = 10
x = 3
y = 4

8y = 32

rarns: Newbie | Next Rank: 10 Posts; Posts: 7; Joined: Wed Jun 01, 2011 3:33 am; Thanked: 1 times

by rarns » Wed Jun 08, 2011 12:35 pm

What I found easiest:

80 = 8x + 16y

7 = x + y, hence: x = 7 - y

Plug in: 80 = 8(7-y) + 16y
24 = 8y
3 = y,

So, x = 4, & 8(4) = 32

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