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

Answer:

Let the number of mangoes A has, be x

and the number of mangoes B has , be y .

∴30+x=2(y−30)⟶(i) ,as A says

and , 10+y=3(x−10)⟶(ii) ,as B says  

On simplification ,

x−2y+90=0⟶(iii)

−6x+2y+80=0⟶(iv)

On adding (iii) and (iv),

−5x+170=0

⇒x=34 mangoes.

putting x in (i),

34−2y+90=0

2y=124

y=62 mangoes.

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Answer 2

Answer:

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