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A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left. When he increased the size of the square by one student, he found that he was short of 25 students. Find the number of students.
Let there be x rows
Then the number of students in each row will also be x
Total number of students x2 + 24
According to the question,
(x + 1)2 – 25 = x2 + 24 using (a + b)2 = a2 + 2ab + b2
x2 + 2x + 1 – 25 – x2 – 24 = 0
2x – 48 = 0
x = 24
Total number of students = 242 + 24 = 576 + 24 = 600
While boarding an aeroplane, a passenger got hurt. The pilot showing promptness and concern, made arrangements to hospitalize the injured and so the plane started late by 30 minutes. To reach the destination, 1500 km away, in time, the pilot increased the speed by 100 km/hour. Find the original speed of the plane. Do you appreciate the values shown by the pilot, namely promptness in providing help to the injured and his efforts to reach in time?