The area of a trapezium is 408 cm^{2} and the distance between its parallel sides is 24 cm. If one of the parallel sides is of length 16 cm, find the length of the other side.

Two circles with radii of 3 and 9 are drawn with the same center. The smaller inner circle is painted black, and the part outside the smaller circle and inside the larger circle is painted purple. What is the ratio of the areas painted purple to the area painted black?

The mean of ^@ 70 ^@ numbers was found to be ^@ 63 ^@. Later on, it was detected that a number ^@ 44 ^@ was misread as ^@ 14 ^@. Find the correct mean of the given numbers.

A coin is tossed ^@ 300 ^@ times and it is found that head comes up ^@ 267 ^@ times and tail ^@ 33 ^@ times.
If a coin is tossed at random, what is the probability of getting a head?

In an exam with two subjects, 60% passed the first subject, and 50% passed the second subject. 10% failed in both the subjects. If 164 passed in both subjects, then how many wrote the exam?

The Autorickshaw fare in Rome is € 20 for the first kilometer and € 13 per kilometer for subsequent distance covered. If distance is represented as d, and fare is represented as f, find the linear equation for this relationship.