This is a question on the concept of Proportionality. Note that in questions related to this concept, there will always be a constant called the constant of proportionality which is required to convert the proportionality expression to an equation.
The cost of the slab, c, is proportional to its thickness, t, and also proportional to the square of its length viz., \(l^2\) i.e.
c ∝ t * \(l^2\).
To convert the above expression to an equation, we introduce a constant of proportionality, say k. Therefore,
c = k*t\(l^2\).
We need to find the cost of a square slab of length 3 meters and of thickness 0.1 meters. Effectively, we need to find the value of c when t = 0.1 and l = 3, for which we need the value of k.
From statement I alone, we know the difference in the costs of two slabs whose dimensions are given.
This is sufficient to develop an equation containing k and to solve for k. Statement I alone is sufficient.
If c1 = k * 0.2*4 and c2 = k* 0.1*4, we know c1= c2 +160. This is sufficient to find the value of k.
Since statement I alone is sufficient, answer options B, C, and E can be eliminated. Possible answer options are A or D.
From statement II alone, we know the difference in the costs again and we have already done something similar in statement I. So, time to SAVE TIME and conclude that statement II alone is sufficient instead of trying to work out the equations.
Statement II alone is sufficient. Answer option A can be eliminated.
The correct answer option is D.
Whenever the opportunity to save time presents itself, grab it with both hands. And do not forget that a lot of DS questions actually present you with such opportunities, if only you are ready to take them.
Hope that helps!
Arvind.