Question

Adnan wishes to distribute $6$ sweets to each of his $42$ classmates on his birthday. But some students were absent on his birthday and he distributed $9$ sweets each amongst the present students in the class. Find out the number of students who were absent.

Answer 1

Hint: We will find the number of sweets Adnan bought to be distributed among his classmates by multiplying the number of sweets distributed to each student and the total number of students. Then we will use the unitary method to find the number of students present on Adnan’s birthday. Then subtract the obtained number by the total number of students and we’ll get the answer.

Complete step-by-step answer:
Given, the total number of classmates= $42$
Adnan wishes to distribute $6$ sweets to each student so the total number of sweets he brought for his classmates =$42 \times 6 = 252$
Now, since some students were absent he distributed $9$ sweets each amongst the present students in the class. So we will use the unitary method to find the number of students who were present in the class on Adnan’s birthday.
$ \Rightarrow 9$ sweets were given to $1$ student
So $1$ sweet was given to $\dfrac{1}{9}$ students
$ \Rightarrow 252$ sweets were given to $\dfrac{{252}}{9}$ students
So on solving, we get-
$ \Rightarrow 252$ sweets were given to $28$ students
Since the number of students present that day=$28$
Then to find the number of students absent that day we will subtract the number of present students from the total number of students.
$ \Rightarrow $ Number of students who were absent=$42 - 28$
On subtraction, we get-
$ \Rightarrow $ Number of students who were absent=$14$
The number of students absent on Adnan’s birthday is $44$ .

Note: We can also solve this question by directly finding the number of students absent on Adnan’s birthday-
Let the number of students absent on Adnan’s birthday be x. Then the number of students present that day =$42 - x$
Adnan wishes to distribute $6$ sweets to each student so the total number of sweets he brought for his classmates =$42 \times 6 = 252$
Now the number of sweets when Adnan wished to distribute will be equal to the number of sweets he distributed that day so we can write-
$ \Rightarrow 252 = \left( {42 - x} \right)9$
On solving, we get-
$ \Rightarrow 252 = 378 - 9x$
On further solving, we get-
\[ \Rightarrow 9x = 378 - 252 = 126\]
On further solving, we get-
$ \Rightarrow x = \dfrac{{126}}{9} = 14$