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?
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Answer:
(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=3105
y=62
x-2×62+90=0
x-124+90=0
x-34=0
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Answer:
A has 34 mangoes and B has 62 mangoes
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