Question

A and B both have some pencils . If A gives 10 pencils to B, then B will have twice as many as A. And if B gives 10 pencils to A , then they will have the same number of pencils . How many pencils does each have ? ​

Answer 1

Answer:

A = 50

B = 70

Step-by-step explanation:

Let A have x pencils and B have y.

As per the statement, "If A gives 10 pencils to B, then B will have twice as many as A" =>2(x−10)=y+10=>2x−y=30 --- (1)

And, as per "if B gives 10 pencils to A, then they will have the same number of pencils" => x+10=y−10=>x−y=−20 --- (2)Subtracting equation (2)

from (1), we get x=50

Substituting x=50 in the

equation (2), we get 50−y=−20=>y=70

Answer 2

Answer:

A=50

B=70

Step-by-step explanation:

Let A and B have x and y pencil.

Then, let's look at both the cases:

Case I

A gives 10 pencils to B (y+10),B gains 10 pencil

And A lose 10 pencils(x-10)

Then,it is given that B has twice as many as A

Then B=2xA

Y+10=2(x-10)_____i

Case II

B gives 10 pencils to A (x+10),A gains 10 pencil

and B lose 10 pencils(y-10).

But still, it is given that both A and B has equal number of Pencils.

That means: x+10=y-10 _____ii

Now solving i and ii:

Solving i

Y+10=2(x-10)

=y+10=2x-20

=y-2x=-30

=y=2x-30

Solving ii

x+10=y-10

y=x+20

Now

x+20=2x-30. (both are equal to y, see above)

-x=-50

x=50

And y= 50+20=70

A has 50 pencils and B has 70