Questions

The construction of the world’s largest optical telescope has started in northern Chile, which is expected to begin operating in 2024. The Extremely Large Telescope (ELT) is being built by the European Southern Observatory (ESO) and will have a main mirror that is 39m in diameter. The telescope will be positioned on top of Cerro Armazones – a 3046-metre long mountain Chile. It will tackle a wide range of scientific challenges, including probing Earth-like exoplanets for signs of life, studying the nature of dark energy and dark matter, and observing the universe’s early stages to explore humans’ origins.

Let the two digits be x & y

From given data in the question, we get

x + y = 3(x - y)

x + y = 3x - 3y

=> 2x = 4y

x/y = 2/1

For having the 2:1, numbers satisfying are

12, 21, 24, 42, 36, 63, 48, 84

From this 36 is eleminated because it is a perfect square and no others are prime or perfect squares.

Hence, there exists 7 such 2-digit numbers => 12, 21, 24, 42, 63, 48, 84.