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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
To find:
(1) Total mangoes of A.
(2) Total mangoes of B.
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 - 2xx62+90 =0`
`x - 124 + 90 =0`
`x - 34 = 0`
`x = 34`
Hence A has 34 mangoes and B has 62 mangoes.
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