which paint will be cheaper

[funtesting]

A home owner must pick between paint A which costs $6.00 per liter, and paint B, which costs $4.50 per liter. Paint B takes one-third longer to apply than paint A. If the home owner must pay labor costs, which of the two paints will be cheaper to apply?

1. The ratio of the area covered by one liter of paint A to the area covered by paint B is 4:3.

2. Paint A will require 40 liters of paint and 100 hours of labor.

The answer given is E. I think it is A because using the ratio you can definitely tell which paint would cost more overall.

Could someone please explain?

[sooraj_j]

I agree. If the question is as you have given it, A should be sufficient

If the total area to be paintef is t sq. m.
and A paints x sq m per liter and B paints y sq m per lite as per the ratio given in A, then

total cost of with A = t/x * 6 + Labor costs (L)
total cost of with B = t/y * 4.5 + Labor costs*4/3

Now, x/y = 4/3; y = 3/4 * x
So, A's cost = t/x * 6 + L
B's cost = ( t/(3/4)x ) * 4.5 + L*4/3 = t/x * 6 + L*4/3

Clearly, B costs more only because the labor costs are more.

Is there something I missed?

[andynags]

can we assume that labor costs are related to area covered?

Originally posted by sooraj_j

I agree. If the question is as you have given it, A should be sufficient

If the total area to be paintef is t sq. m.
and A paints x sq m per liter and B paints y sq m per lite as per the ratio given in A, then

total cost of with A = t/x * 6 + Labor costs (L)
total cost of with B = t/y * 4.5 + Labor costs*4/3

Now, x/y = 4/3; y = 3/4 * x
So, A's cost = t/x * 6 + L
B's cost = ( t/(3/4)x ) * 4.5 + L*4/3 = t/x * 6 + L*4/3

Clearly, B costs more only because the labor costs are more.

Is there something I missed?

[shri62]

My pick would be "A" since its sufficient to answer the question.

Statement A --> Since the ratio of the area covered is 4:3 .

Hence to cover the same area , 1.33 litre of paint B will cover same area as that covered by 1 litre of paint A .

Hence cost wise both will be equivalent i.e paint B 1.33 litre cost $6.00 .

Hence from statement 1 we can conclude that since both pain cost wise per litre will be the same and knowing the fact that paint B takes one-third longer to apply so more labor cost..hence B will be expensive.

Statement 2 --> very straight forward ...
Since we know that paint B takes 0ne-third longer to apply ..and paint A is taking 100 hours so paint B will take 133 hours.
Also 40 litres will be used so total saving in money wil be :
(6-4.50)*40 = $60
and we know it will take 33 hours more to apply paint "B".
However we dont know how much is this "33" extra hours gonna cost us...we just know that we will save $60 by selecting paint B but it might be expensive in labor or "33" hrs of labor might be less than $60...we have no information on that.

so the right answer is "A" .

[sharadaprasad]

A is the answer.

BTW, the stem also has the labour cost - $36