Question

In X class, if three students sit on each bench, one student will be left. If four students sit on each bench, one bench will be left. Find the number of students and the number of benches in that class.

Answer 1

Dear Student,

Answer:

Number of benches in the class 10th are 5,
Number of students in the class 10th are 16.

Solution:

let the number of benches in the class 10th are y,
and number of students in the class 10th are x

according to the question

if three students sit on each bench, one student will be left,so equation will be

3y +1 = x ...eq1

If four students sit on each bench, one bench will be left,so equation will be

4(y-1)= x ...eq2

Simplify eq 1 and 2

-x +3y = -1

-x +4y = 4

subtract both eq

-x +3y+x-4y = -1-4

-y = -5

y = 5

put the value of Y in either equation 1 or 2

-x+3(5)+1 = 0

-x = - 16

x= 16

So, the number of benches in class 10th are 5 and the number of students in class 10th are 16.

hope it helps you.

Thanks for asking such a nice question.

Answer 2

HELLO DEAR,

let the number of benches in the class 10th are y,

and number of students in the class 10th are x

according to the question

if three students sit on each bench, one student will be left,so equation will be

3y + 1 = x ------------( 1 )

If four students sit on each bench, one bench will be left,

so equation will be

4(y -1) = x

x = 4y - 4 -----------( 2 )

from--------------( 1 ) & -----------( 2 )

3y + 1 = 4y - 4

4y - 3y = 4 + 1

y = 5 [ put in --------( 1 ) ]

x = 3(5) + 1

x = 15 + 1

x = 16

So, the number of benches in class 10th are 5 and the number of students in class 10th are 16

I HOPE ITS HELP YOU DEAR,

THANKS