Who is Correct ?

Ram does not want to prove Ram wrong. Wait … is this confusing?

Surface area of a cube = $6a^2$ (as there are 6 surfaces each with area $a^2$ ).

Initially, there is only one cube, so $6a^2 = 150 \implies \boxed{{\color{#3D99F6}a^2} = 25}$

But now two cubes are joined, that means we should neglect one surface from each cube (the surface of contact between the two) to get the new surface area.

$\implies 2(6a^2) - 2(a^2) = 10{\color{#3D99F6}a^2}$

$\therefore \text{New Surface Area} = 10 \times {\color{#3D99F6}25} = \boxed{\color{#20A900}250}$

Hence, Ram made the correct statement

Since Ram wants to test Bob if he can get the correct answer, Ram definitely should know what is the correct answer. So what Ram says is inevitably true. Hence, the answer will be 250.

The cube has 6 sides, surface area of 5 sides of the cube is (5/6)*150=125 square cm.

Therefore, new surface area of required cube is 2*125=250 square cm. Hence, Ram 's statement is true.

Two cubes have 12 faces, but when the 2 cubes are join as seen in the picture you see only 10 faces. To calculate how much is a faces divide $150\text{ cm}^2$ (the surface area of a cube) on 6(the faces of a cube) and get 25 one face of a cube. 25 x 10 = $250\text{cm}^2$ (the new surface area). Ram's sentence is right.