CAT 1996 — QA Question 6
Direction: Answer the questions based on the following information.
In a locality, there are five small cities: A, B, C, D and E. The distances of these cities from each other are as follows.
AB = 2 km AC = 2km AD > 2 km AE > 3 km BC = 2 km
BD = 4 km BE = 3 km CD = 2 km CE = 3 km DE > 3 km
A wooden box (open at the top) of thickness 0.5 cm, length 21 cm, width 11 cm and height 6 cm is painted on the inside. The expenses of painting are Rs. 70. What is the rate of painting per square centimetres?
Answer & solution
- A
Re 0.7
- B
Re 0.5
Re 0.1
- D
Re 0.2
As it can be seen from the diagram, because of the thickness of the wall, the dimensions of the inside of the box is as follows: length = (21 – 0.5 – 0.5) = 20 cm, width
= (11 – 0.5 – 0.5) = 10 cm and height = (6 – 0.5) = 5.5 cm.
Total number of faces to be painted = 4 walls + one base (as it is open from the top).
The dimensions of two of the walls = (10 × 5.5), that of the remaining two walls = (20 × 5.5) and that of the base
= (20 × 10).
So the total area to be painted = 2 × (10 × 5.5) + 2 × (20 × 5.5) + (20 × 10) = 530 cm2.
Since the total expense of painting this area is Rs. 70, the rate of painting = = 0.13 = Re 0.1 per sq.cm. (approximately).