Raincoats and umbrellas

[hemant_rajput]

Q15 . On 26th July Mumbai was flooded , Rain shield enterprise is in the business of manufacturing umbrellas and raincoats. An umbrella can shield 2 people while a raincoat can shield 1 person. People under an umbrella can walk 1/3rd the speed of a person wearing a raincoat. The cost of an umbrella and cost of raincoat are in the ration 2:5. Points A and B are 100 m apart and it takes 20 min for a person wearing a raincoat to travel the distance . At the max how many people will be transported today from A to B, if only 1000/- is available for transporting 20 people? Cost of traveling time is 2/- per min per head(assume cost of Raincoat to be 100/-)
a. 6
b. 7
c. 4
d. 11
e. 16
[spoiler]oa:b[/spoiler]

[vkb001]

Let no. of umbrella's bought be u, and no. of raincoats bought be r.

No. of people who can travel using umbrella = 2u
No. of people who can travel using raincoat = r

Speed of people using raincoat = 100/20 = 5 m/min
Speed of people using umbrella = 1/3 * 5 = 5/3 m/min

Cost of raincoat = Rs.100
Cost of umbrella = Rs. 40 (calculated from the cost ratio of 2:5)

Total cost of getting umbrellas and moving people = u*(2 people/umbrella)*(Rs.2/min)*(60 min travel time) + u*(Rs.40 purchase cost) = 240u + 40u = 280u
Total cost of getting raincoats and moving people = r*(1 people/raincoat)*(Rs.2/min)*(20 min travel time) + r*(Rs.100 purchase cost) = 140r

Grand total = 280u + 140r should be equal to Rs.1000 to maximize the no. of people benefiting from the purchase.

280u + 140r = 1000 (at maximum)
=> 2u + r = 7.14 (at maximum) ---- Equation 1

But, (2u+r) is also the number of people who'd be able to travel. From Eq. 1, we know that at maximum, that can be 7.14 or 7 people.

[Tommy Wallach]

Whoa! Is this supposed to be a GMAT question, or to somehow help with GMAT skills? Just to be super-clear, it is not, and does not! The problem with unrealistic GMAT question is that they might send your studies off in weird directions. Worse than that, you might actively develop bad habits. For example, most GMAT questions are predicated on trickery/theory, as opposed to calculation. If you get into the habit of doing calculation to solve, you will often end up on the wrong path when it comes to a real GMAT question.

There are maximization questions on the GMAT, by the way, but I've never seen one like that. Also, the punctuation has me confused here. What comes after 1000? Is that money?

Hope I don't sound critical; I just want everyone to be studying useful material!

-t

[shenoydevika]

Hemant,

Is this a CAT/XAT question? It seems like one of those overly complicated CAT questions.