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Question

6. The ages of the students of a class are in A.P., whose common difference is 4months. If the youngest boy is 8 years old and the sum of the ages of all the students of the class is 168 years. Find the numbers of students in the class.


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Solution

Step 1. Note the given data.

Given : Age of youngest boy =8years

Common difference in ages of students=4months

Sum of ages of all the students of the class=168years

Let the number of students be n.

Step 2. Find the first term, common difference, and sum in months.

Let, First term isa

a=8years=8×12months=96months.

Common difference d=4months

And sum,

Sn=168years=168×12months=2016months

Step 3. Find the number of students.

The formula for the sum of n terms in A.P is- Sn=n22a+n-1d

The sum of n terms of the AP is Sn=n22×96+n-14

=n2192+4n-4=n2188+4n=n2×294+2n=94n+2n2

Step 4. Solve using a quadratic equation.

Now, we put the values as-

94n+2n2=20162n2+94n-2016=0n2+47n-1008=0n2+63n-16n-1008=0

n(n+63)-16(n+63)=0(n+63)(n-16)=0Eitheror,n+63=0n-16=0n=-63n=16

nshouldn't be negative.

Hence, the number of students in the class is 16.


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