Q.1 Some students have to be seated in some rows, such that an equal number of students are seated in each row. If there are 13 rows 3 students will be left out and if there are 21 rows, 11 students will be left out. How many students will be left out if there are 19 rows and less than 300 students?
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Q.1 Some students have to be seated in some rows, such that an equal number of students are seated in each row. If there are 13 rows 3 students will be left out and if there are 21 rows, 11 students will be left out. How many students will be left out if there are 19 rows and less than 300 students?
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Solution
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Let the number of rows be x and number of students in a row be y.
Total students of the class= Number of rows × Number of students in a row
=x×y=xy
Case 1
Total number of students =(x−1)(y+3)
⇒xy=(x−1)(y+3)=xy−y+3x−3
⇒3x−y−3=0
⇒3x−y=3..... (i)
Case 2
Total number of students=(x+2)(y−3)
⇒xy=xy+2y−3x−6
⇒3x−2y=−6..... (ii)
Subtracting equation (ii) from (i),
⇒(3x−y)−(3x−2y)=3−(−6)
⇒−y+2y=3+6
⇒y=9
By substituting value of y in (i), we get
⇒3x−9=3
⇒3x=9+3=12
⇒x=4