In an election between two candidates, \(12\%\) votes did not cast their vote. \(\left(\dfrac{1}{6}\right)^{\text{th}}\) of the votes casted were found to be invalid. The winner obtained \(55\%\) of the valid votes and won the election by 36542 votes. Find the total number of voters registered.

If the adjacent sides of a rectangle are increased by \(35\%\) and \(20\%\), respectively, then by what percent will its area increase?

Find the LCM of the numbers: \(\dfrac{4}{9},\ \dfrac{8}{15},\ \dfrac{6}{9},\ \dfrac{12}{21},\ \dfrac{14}{33}\)

What smallest number should be subtracted from 81025 to get a perfect square number?

The LCM of two numbers is 15 times their HCF. If the sum of their LCM and HCF is 160 and one of the numbers is 50, then what is the other number?

Simplify: \(15+60\div15\times2-1\)

On simple interest a certain sum amounts to ₹ 14061 in 6 years and to ₹ 16023 in 8 years on the same rate of interest. The rate of interest per annum is:

Two years ago, the ages of Rekha and Shruti were in the ratio \(2:3\). Three years hence, the ratio will become \(3:4\). How old will Shruti be after 8 years from now?

A certain sum on compound interest becomes ₹ 19573 at \(15\%\) per annum in 2 years. Find the compound interest on the same sum at \(10\%\) per annum in 2 years.