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Q.

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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a

A:34mangoes; B: 62mangoes

b

A:22mangoes; B: 48mangoes

c

A:38mangoes; B: 90mangoes

d

A:56mangoes; B: 92mangoes  

answer is A.

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Detailed Solution

let A has x mangoes and B has y mangoes.
According to the question
⇒(x+30)=2(y-30)
⇒x+30=2y-60
⇒x-2y=-90………(1)
⇒3(x-10)=y+10
⇒3x-30=y+10
⇒3x-y=40……(2)
Multiply equation (2) by 2,
⇒6x-2y=80………(3)
Subtract equation (1) and equation (2),
⇒5x=170
⇒x=34
Substituting x=34 in equation (1),
⇒34-2y=-90
⇒-2y=-124
⇒y=62
A has 34mangoes
B has 62mangoes
Therefore, option (1) is correct.
 
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