A solid cube, whose diagonal is $$ 128 {\ sqrt {2}} \ cm $$, is molded to form a cuboid. The length and width of the cuboid are 512 cm and 160 cm, respectively. What is the height of the cuboid?

A ladder 20 m long is leaning against a vertical wall. It makes an angle of 30° with the ground. How high on the wall does the ladder reach?

The angle of elevation of ladder leaning against a house is 60° and the foot of the ladder is 6.5 meters from the house. The length of the ladder is 

A pipe can fill a tank in 72 minutes. But there is a leak in the bottom of the tank due to which the tank is filled in 18 minutes more. Find in how many hours the leak can empty a full tank ?

A hemispherical bowl of internal diameter 54 cm contains a liquid. The liquid is to be filled in cylindrical bottles of radius 3 cm and height 9 cm, then find the number of bottles that can be filled?

A book can be read in 40 days if 7 pages are read every day. If the book needs to be read in 8 days. How many pages should be read every day? 

The simple interest on ₹ 4,000 in 3 years at the rate of x % per annum equals the simple interest on ₹ 5,000 at the rate of 12% per annum in 2 years. The value of x is 

If the diameter of a wire is decreased by 10% by how much per cent (approximately) will the length be increased to keep the volume constant?