Ratio problem

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pavan555: Newbie | Next Rank: 10 Posts; Posts: 2; Joined: Tue Apr 24, 2012 7:55 am

by pavan555 » Tue Apr 24, 2012 7:58 am

Can you please answer this urgently

Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $40. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is
A. 120
B. 200
C. 60
D. 24
E. 36

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Source: Beat The GMAT — Problem Solving | Tue Apr 24, 2012 7:58 am

aneesh.kg: Master | Next Rank: 500 Posts; Posts: 385; Joined: Mon Apr 16, 2012 8:40 amFollowed by: 29 members; Location: Pune, India; Thanked: 186 times

by aneesh.kg » Tue Apr 24, 2012 9:12 am

Tom : Dick : Harry : Total = 100 : 60 : 40 : 200 = T : D : H : 120
100 : 200 = T : 120, or T = 60
40 : 200 = H : 120, or H = 24
T - H = 60 - 24 = 36

(E) is the answer.

Aneesh Bangia
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GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Tue Apr 24, 2012 3:07 pm

pavan555 wrote:Can you please answer this urgently

Tom, Dick and Harry went for lunch to a restaurant. Tom had $100 with him, Dick had $60 and Harry had $40. They got a bill for $104 and decided to give a tip of $16. They further decided to share the total expenses in the ratio of the amounts of money each carried. The amount of money which Tom paid more than what Harry paid is
A. 120
B. 200
C. 60
D. 24
E. 36

T : D : H = 100:60:40 = 10:6:4 = 5:3:2.
The sum of the values in the ratio = 5+3+2 = 10.
The total amount paid = 104+16 = 120.
Since the total amount paid is 12 times the sum of the values in the ratio, all of the values in the ratio must be multiplied by a factor of 12:
T : D : H = 12(5:3:2) = 60:36:24.
Thus, T-H = 60-24 = 36.

The correct answer is E.

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