Question

A and B each have a certain number of mangoes. A says to B, "if you give 30 of your mangoes, I will have twice as many as left with you." B replies, "if you give me 10, I will have thrice as many as left with you." How many mangoes does each have?

Answer 1

Suppose A has x mangoes and B has y mangoes,

According to the given conditions,

x + 30 = 2(y – 30)

x + 30 = 2y – 60

x – 2y + 30 + 60 = 0

x – 2y + 90 = 0

y + 10 = 3(x – 10)

y + 0 = 3x – 30

y – 3x + 10 + 30 = 0

y + 3x + 40 = 0

y – 3x + 10 + 30 = 0

y – 3x + 40 = 0

Multiplying eq. 1 by 3

3x + 6y + 270 = 0      ...(3) and

Now adding eq. (2) and eq. (3)

5y = 310

`y = 310 /5`

`y = 62`

x – 2 × 62 + 90 = 0

x – 124 + 90 = 0

x – 34 = 0

x = 34

Hence, A has 34 mangoes and B has 62 mangoes.