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8. A teacher on attempting to arrange the students for mass drill in the form of a soldsquare found that 24 students were left. When he increased the size of the squareby one student, he found that he was short of 25 students. It is required to find thenumber of students. |
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Answer» Given:A teacher attempts to arrange his students in the form of a solid square.ii24 students were left.iiiiWhen he increased the size of the square by 1, he was short of 25 students. We need to find the number of students. Let the number of rows of students bexx.Since the number of columns of students is alsoxx, the number of students in each row is thusxx. Conditioniigives us:The total number of students =x2+24x^2 + 24. Conditioniiiigives us:(x+1)2−25=x2+24(x + 1)^2 - 25 = x^2 + 24∴x2+2x+1−25=x2+24\therefore x^2 + 2x + 1 - 25 = x^2 + 24 (using(a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2)∴x2+2x−24=x2+24\therefore x^2 + 2x - 24 = x^2 + 24∴2x−48=0\therefore 2x - 48 = 0∴x=24\therefore x = 24 Conditioniigives us:The total number of students =242+24=60024^2 + 24 = 600. Therefore, there were a total of 600 students. |
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