XAT 2010 Question 96

Question 96

A tank internally measuring 150cm × 120cm × l00cm has $$1281600cm^{3}$$ water in it. Porous bricks are placed in the water until the tank is full up to its brim. Each brick absorbs one tenth of its volume of water. How many bricks, of 20cm × 6cm × 4cm, can be put in the tank without spilling over the water?

Solution

Volume of tank = $$150 \times 120 \times 100 = 18,00,000 cm^3$$

Volume of water in the tank = $$12,81,600 cm^3$$

Volume to be filled in the tank = $$18,00,000 - 12,81,600 = 5,18,400 cm^3$$

Let the number of bricks to be placed in the tank = $$x$$

Volume of $$x$$ bricks = $$x \times 20 \times 6 \times 4 = 480x cm^3$$

Each brick absorbs $$(\frac{1}{10})^{th}$$ of its volume in water

=> $$x$$ bricks will absorb = $$\frac{480 x}{10} = 48x cm^3$$

$$\therefore$$ $$5,18,400 + 48x = 480x$$

=> $$480x - 48x = 432x = 5,18,400$$

=> $$x = \frac{518400}{432} = 1200$$



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