Question

A and B have some pens . If A give 20 pens to B, then B will have thrice as many as A. And if B gives 20 pens to A, then they will have same numbers of pens , how many does each have.​

Answer 1

Answer:

Question:-

• A and B have some pens . If A give 20 pens to B, then B will have thrice as many as A. And if B gives 20 pens to A, then they will have same numbers of pens , how many does each have.

Answer :-

Given :-

• A and B have some pens . If A give 20 pens to B, then B will have thrice as many as A and if B gives 20 pens to A, then they will have same numbers of pens.

To Find :-

• The number of pens A and B have.

Solution :-

Let A have 'x' number of pens and B have 'y' number of pens.

★ Case :- 1.

If A give 20 pens to B, then

⇛ A have (x - 20) pens.

and B have (y + 20) pens.

★ According to statement

B will have thrice as many as A.

⇛y + 20 = 3 × (x - 20)

⇛y + 20 = 3x - 60

⇛y = 3x - 80 .............(1).

★ Case :- 2.

If B gives 20 pens to A,

⇛A have (x + 20) pens,

and B have (y - 20) pens.

★ According to statement

B and A have same number of pens.

⇛ y - 20 = x + 20

⇛ y = x + 40...................(2)

Now, equate (1) and (2), we get

$\bf\implies \:3x - 80 = x + 40$

$\bf\implies \:3x - x = 80 + 40$

$\bf\implies \:2x = 120$

$\bf\implies60 \:{\cancel\dfrac{120}{2}=x}$

Put x = 60 in equation (2), we get,

$\bf \:y = 60 + 40$

$\bf\implies \:y = 100$

$\bf\implies \: A \: has \: 60 \: pens \: and \: B \: has \: 100 \: pens.$

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Answer 2

Step-by-step explanation:

Solution :-

Let A have 'x' number of pens and B have 'y' number of pens.

★ Case :- 1.

If A give 20 pens to B, then

⇛ A have (x - 20) pens.

and B have (y + 20) pens.

★ According to statement

B will have thrice as many as A.

⇛y + 20 = 3 × (x - 20)

⇛y + 20 = 3x - 60

⇛y = 3x - 80 .............(1).

★ Case :- 2.

If B gives 20 pens to A,

⇛A have (x + 20) pens,

and B have (y - 20) pens.

★ According to statement

B and A have same number of pens.

⇛ y - 20 = x + 20

⇛ y = x + 40...................(2)

Now, equate (1) and (2), we get

\bf\implies \:3x - 80 = x + 40⟹3x−80=x+40

\bf\implies \:3x - x = 80 + 40⟹3x−x=80+40

\bf\implies \:2x = 120⟹2x=120

\bf\implies60 \:{\cancel\dfrac{120}{2}=x}⟹60

2

120

=x

Put x = 60 in equation (2), we get,

\bf \:y = 60 + 40y=60+40

\bf\implies \:y = 100⟹y=100

\bf\implies \: A \: has \: 60 \: pens \: and \: B \: has \: 100 \: pens.⟹Ahas60pensandBhas100pens.

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