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, we have

x + 30 = 2(y - 30)

=> x + 30 = 2y - 60

=> x - 2y = -60 - 30

=> x - 2y = -90 ....(i)

And y + 10 = 3(x - 10)

=> y + 10 = 3x - 30

=> 10 + 30 = 3x - y

=> 3x - y = -40 ....(ii)

Multiplying equation (i) by 3 and equation (ii) by 1, we get

3x - 6y = -270 ....(iii)

3x - y = 40 ....(iv)

Subtracting equation (iv) by equation (iii), we get

-6y - (-y) = -270 - 40

=> -6y + y = -310

=> -5y = -310

`=> y = 310/5 = 62`

Putting x = 62 in equation (i), we get

`x - 2 xx 62 = -90`

=> x - 124 = -90

=> x = -90 + 124

=> x = 34

Hence, A has 34 mangoes and B has 62 mangoes