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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?
Solution
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
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