Question

30 student have certain money now one more student with Rs 120 joins then so that average inceeases by Rs 1 find out the new average of 31 students

Answer 1

${ \boxed {\boxed{ \bold \red{ANSWER}}}}$

${ \boxed {\boxed{ \bold \red{GIVEN}}}}$

30 students have certain average money, now one more students with Rs 120 join them so that the new average increased by Rs 1.

${ \boxed {\boxed{ \bold \red{TO \: DETERMINE}}}}$

The new average of all 31 students

${ \boxed {\boxed{ \bold \red{EVALUATION}}}}$

Let the average money of 30 students = Rs x

Then total money of 30 students = Rs 30

Now one more students with Rs 120 join them

So the total amount becomes

= Rs ( 30x + 120 )

Now it is given that the new average increased by Rs 1

So the new average = Rs ( x + 1 )

In that case total amount of money

= Rs 30( x + 1 )

So by the given condition

$\sf{31(x + 1) = 30x + 120}$

$\sf{ \implies \: 31x +31 = 30x + 120}$

$\sf{ \implies \: 31x - 30x = 120 - 31}$

$\sf{ \implies \: x = 89}$

Hence new average of all 31 students

= Rs ( 89 + 1 )

= Rs 90

${ \boxed {\boxed{ \bold \red{FINAL \: ANSWER}}}}$

The new average of all 31 students

= Rs 90