Question

Urgent Question !!!

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In a class of 15 students, on an average, each student got 12 books. If exactly two students received same number of books, and remaining student books average be an integer then which of the following could be the number of books received by each of the two students who received same number of books?

(1) 11

(2) 15

(3) 20

(4) 25

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Answer 1

$\underline{\underline{ \large{ \mathfrak{Solution : }}}}$



$\underline{\textsf{Given : }} \\ \\ \mathsf{\implies No. \: of \: students \: = \: 15} \\ \\ \mathsf{\implies Average \: book \: they \: got \: = \: 12} \\ \\ \mathsf{We \: know \: that : } \\ \\ \mathsf{\implies Average \: = \: \dfrac{Sum \: of \: all \: observations}{No. \: of \: observation}} \\ \\ \textsf{Now : } \\ \\ \mathsf{\implies 12 \: = \: \dfrac{No. \: of \: total \: books}{15}} \\ \\ \mathsf{\implies 12 \: \times \: 15 \: = \: No. \: of \: total\: books } \\ \\ \mathsf{\therefore \quad No. \: of \:total\: books \: = \: 180}$




$\textsf{According to question : }$




$\textsf{Two students got equal number of books. Let}\\ \textsf{ each of them got x books , }\\ \textsf{so total books got by them is 2x. Now,}\\ \textsf{ according to question the average books got}\\ \textsf{ by remaining student is an integer.}$




$\textsf{Now : } \\ \\ \mathsf{\implies No. \: of \: students \: = \: 15 \: - \: 2 \: = \: 13} \\ \\ \mathsf{\implies No. \: of \: total \: books \: = \: 180 \: - \: 2x}$




$\mathsf{We \: know \: that : } \\ \\ \mathsf{\implies Average \: = \: \dfrac{Sum \: of \: all \: observations}{No. \: of \: observation}}$




$\mathsf{\implies Average \: = \: \dfrac{180 \: - \: 2x}{13}} \\ \\ \\ \textsf{When , x = 11 } \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 2 \: \times \: 11}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 22}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{158}{13} \: = \: 12.154(Approx)} \\ \\ \\ \textsf{Doesn't Satisfy the given condition.}$



$\textsf{When , x = 15 } \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 2 \: \times \: 15}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 30}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{150}{13} \: = \: 11.538(Approx)} \\ \\ \\ \textsf{Doesn't Satisfy the given condition.}$




$\textsf{When , x = 20 } \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 2 \: \times \: 20}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 40}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{140}{13} \: = \: 10.769(Approx)} \\ \\ \\ \textsf{Doesn't Satisfy the given condition.}$




$\textsf{When , x = 25 } \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 2 \: \times \: 25}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{180 \: - \: 50}{13}} \\ \\ \\ \mathsf{\implies Average \: = \: \dfrac{130}{13} \: = \: 10} \\ \\ \\ \textsf{ Satisfies the given condition.}$




$\textsf{Therefore, they could receive 25 books each.}$

Answer 2

Heya mate....

Students = 15

Average Books = 12

Average books = total books ÷ no. Of students

12=total ÷ 15

Total = 180

But

2 students got same books

Let both got 2x books so one got x books

Students left are 13 as total - students with same books

Books will be 180 - 2x

Now again

Average = total ÷ no of students

Average = 180-2x/13

Now using hit and trial method of options

Put x= 11

Average = 158÷13

=12.1[not an integer]

Put x= 20

Average = 140/13

=10.7 [ not an integer]

Put x=15

Average = 150/13

=11.5[not sn integer]

Put x=25

Average = 130/13

=10 [an integer]

Therefore 25 is ur answer

@skb