Question

There are 48 students in a class. The age of one of
them is twice that of another. If these 2 are replaced
by 2 others whose ages are 16 years and 11 years,
the average age of the class increases by
1.5 months. Find the age of the younger of the
2 students in years).​

Answer 1

Given :

Total number of students in a class = 48

The age of one of  them is twice that of another

If these 2 are replaced  by 2 others whose ages are 16 years and 11 years,  the average age of the class increases by  1.5 months

To Find :

The age of the younger of the  2 students in years

Solution :

Let The age of younger student = x  years

So, The age of elder student = 2 x  years

∵ Let The average of 48 students = A

i.e   $\dfrac{x_1+x_2+x_3+...............+x_4_8}{48}$ = A

Or, $x_1+x_2+x_3+.................+x_4_8$ = 48 A

∵ The age of two students among 48 students is x years and 2 x years

So, $x_1+x_2+x_3+x_4 + x + 2 x + .................+x_4_8$ = 48 A

Or,  , $x_1+x_2+x_3+x_4 + .................+x_4_6$ = 48 A - 3 x                 .........1

Again

When these two students replace by others  whose ages are 16 years and 11 years,  the average age of the class increases by  1.5 months

So,

   $\dfrac{x_1+x_2+x_3+16 + 11...............+x_4_8}{48}$ = A + $\dfrac{1.5}{12}$

Or,

   $\dfrac{x_1+x_2+x_3+16 + 11...............+x_4_8}{48}$ = A + 0.125

Or,   $x_1+x_2+x_3+x_4 + .................+x_4_6$ + 27 = 48 × ( A + 0.125 )

Or, $x_1+x_2+x_3+x_4 + .................+x_4_6$ = 48 A + 6 - 27

Or, $x_1+x_2+x_3+x_4 + .................+x_4_6$ = 48 A -21                   ..........2

From eq 1 and eq 2

 48 A - 3 x  = 48 A - 21

Or,  3 x = 21

∴        x = $\dfrac{21}{3}$

i.e     x = 7

Put the value of x

So, The age of younger student = x = 7  years

And  The age of elder student = 2 × 7 = 14  year

Hence,  The age of younger student is 7 years  . Answer

Answer 2

Answer:

Let the age of first student is x and other is 2x

Step-by-step explanation:

As, average increased by 1.5

so, Sum = average × number

= 1.5 × 48 months

= 72 months

= 72 ÷ 12

= 6 years

Now, change in average = 16 + 11 - 6

= 21

Here, x + 2x = 21

x = 7

so, age of students are x = 7 year

and 2x = 14 years

and the age of younger student is 7 years