Question

There are two class rooms
A and B. If 10 students are sent from A to B,
the number of students in each room becomes
the same. If 20 students are sent from B to A,
the number of students in A becomes double
the number of students in B. Find the number
of students in each class room.​

Answer 1

❏ Question:-

There are two class roomsA and B. If 10 students are sent from A to B,the number of students in each room becomes the same. If 20 students are sent from B to A ,the number of students in A becomes double the number of students in B. Find the number of students in each class room.

❏ Solution:-

✦ Conditions:-

• If 10 students are sent from A to B,the number of students in each room becomes the same.

•If 20 students are sent from B to A ,the number of students in A becomes double the number of students in B.

✦ To Find:-

• Number of students in class room A.

• Number of students in class rroomB.

✦ Explanation:-

let,

the number of students in class room A is = X.

and,

the number of students in class room A is = Y.

Now, applying the 1'st condition,

$\sf\longrightarrow X-10=Y+10$

$\sf\longrightarrow X-Y=10+10$

$\sf\longrightarrow \boxed{X-Y=20}............(i)$

Now, applying the 2'nd condition,

$\sf\longrightarrow X+20=2\times(Y-20)$

$\sf\longrightarrow X-2Y=-40-20$

$\sf\longrightarrow \boxed{X-2Y=-60}............(ii)$

Now, Doing $eq^n$ [(i)-(ii)] we get;

$\sf\longrightarrow X-Y-X+2Y=20-(-60)$

$\sf\longrightarrow\cancel{ X}-Y-\cancel{X}+2Y=20+60)$

$\sf\longrightarrow\boxed{\large{\red{ Y=80}}}$

Now, putting the value Y=80 in $eq^n$ (i),

we get,

$\sf\longrightarrow X-80=20$

$\sf\longrightarrow X=20+80$

$\sf\longrightarrow\boxed{\large{\blue{ X=100}}}$

∴ number of students in Class A = 100

∴ number of students in Class B = 80

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Answer 2

❏ Question:-

There are two class roomsA and B. If 10 students are sent from A to B,the number of students in each room becomes the same. If 20 students are sent from B to A ,the number of students in A becomes double the number of students in B. Find the number of students in each class room.

❏ Solution:-

✦ Conditions:-

• If 10 students are sent from A to B,the number of students in each room becomes the same.

•If 20 students are sent from B to A ,the number of students in A becomes double the number of students in B.

✦ To Find:-

• Number of students in class room A.

• Number of students in class rroomB.

✦ Explanation:-

let,

the number of students in class room A is = X.

and,

the number of students in class room A is = Y.

Now, applying the 1'st condition,

$\sf\longrightarrow X-10=Y+10$

$\sf\longrightarrow X-Y=10+10$

$\sf\longrightarrow \boxed{X-Y=20}............(i)$

Now, applying the 2'nd condition,

$\sf\longrightarrow X+20=2\times(Y-20)$

$\sf\longrightarrow X-2Y=-40-20$

$\sf\longrightarrow \boxed{X-2Y=-60}............(ii)$

Now, Doing $eq^n$ [(i)-(ii)] we get;

$\sf\longrightarrow X-Y-X+2Y=20-(-60)$

$\sf\longrightarrow\cancel{ X}-Y-\cancel{X}+2Y=20+60)$

$\sf\longrightarrow\boxed{\large{\red{ Y=80}}}$

Now, putting the value Y=80 in $eq^n$ (i),

we get,

$\sf\longrightarrow X-80=20$

$\sf\longrightarrow X=20+80$

$\sf\longrightarrow\boxed{\large{\blue{ X=100}}}$

∴ number of students in Class A = 100

∴ number of students in Class B = 80

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