At most how many spheres of the same size can be placed around a same size sphere at the centre so that they all simultaneously touch the sphere at the centre?

It is 12 o’clock, and the hour and minute hands are aligned exactly one over the other. Both hands move continuously. After how many minutes will they meet again?

A water tank of dimensions 20 cm x 5 cm x 10 cm has 307 cc water in it. A few bricks, each of dimensions 5 cm x 2 cm x 1 cm are fully submerged in the tank. Each brick absorbs 30% of its own volume of water. Just enough bricks are put in, such that the water level rises to comple…

There are some men and some women in a group. Each person shakes hands with exactly one other person in the entire group. After this round of handshakes, eight men and four women find that they shook hands with someone of the same sex. The total number of handshakes exchanged in…

Count the total number of black diamonds in the given pattern. [Figure: see page 5 of source PDF]

How many different ways are there to get from Tile A to Tile I without visiting a tile more than once, if only horizontal and vertical movements are allowed? [Figure: see page 4 of source PDF]

How many pages of size 21 cm x 25 cm can be made from a roll of 48 m x 1.2 m paper? Assume the pages are perfectly cut edge to edge.

A company account book reveals the following figures: Sales | 2,35,126 Gross Profit | 68,799 Administrative Expenses | 2,456 Selling Expenses | 4,789 Calculate the Operating Profit Ratio of the company.

How many tree trunks are there in the given figure? [Figure: see page 5 of source PDF]