Question

A and B each have certain number of oranges. A says to B , if you give me 10 of your oranges , I will have twice the number of oranges left with you. B replies , if you give me 10 of your oranges , i will have the same number of oranges as left with you. find the number of oranges with a and b.

Answer 1

Solution :-

Let A has 'x' number of oranges and B has 'y' number of oranges respectively.

Situation 1

If B gives 10 of his oranges to A then A will have twice the number of oranges as left with B.

⇒ (x + 10) = 2(y - 10)
⇒ x + 10 = 2y - 20
⇒ 2y - x = 30 ..................(1)

Situation 2

If A gives 10 of his oranges to B then B will have same number of oranges as left with A.

⇒ (x - 10) = (y + 10)
⇒ - y + x = 20 .....................(2)

Adding (1) and (2), we get.

  2y - x = 30
 - y + x = 20
___________
   y       = 50
___________

The value of y is 50.

Putting the value of y = 50 in (2), we get.

- y + x = 20
- 50 + x = 20
x = 20 + 50
x = 70

Therefore, A has 70 oranges and B has 50 oranges.

Answer 2

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Let, us suppose that A has x oranges.

And b as y oranges.

According to the question :-

x+10 = 2(y-10)

⇒ x - 2y + 30 = 0 --- ( 1 )

And,

y+10 = x - 10

⇒ x-y-20 = 0 --- ( 2 )

Subtract (1) from (2) we get :-

-y + 50 = 0

y = 50.

Put, the value of "y" in eq. ( 1 ) :-

Than we get,

x = 70.

Hence, A has 70 oranges and Bhas 50 oranges.