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A and B has a certain …

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A and B has 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 you". How many mangoes does each have?

Posted by Muddit Popli 6 years, 6 months ago

CBSE > Class 10 > Mathematics

1 answers

Sia ? 6 years, 6 months ago

Assume A has x mangoes and B has y mangoes.
As per given condition if B gives 30 then A will have twice as many as left by B.
(x + 30) = 2(y - 30)
{tex}\Rightarrow{/tex}x + 30 = 2y - 60
{tex}\Rightarrow{/tex} x = 2y - 90....(1)
And if A gives 10 mangoes to B, then B will have thrice as many as left by A.
3(x - 10) = (y + 10)
{tex}\Rightarrow{/tex} 3x = y + 40 ....(2)
{tex}\Rightarrow{/tex} 3(2y - 90) = y + 40 (using x from Eq. 1)
{tex}\Rightarrow{/tex} 6y - 270 = y + 40
{tex}\Rightarrow{/tex} 6y - y = 310
{tex}\Rightarrow{/tex} y = 62
Put y = 62 in (1)
So, x = 124 - 90 = 34
Therefore A has 34 mangoes and B has 62 mangoes.

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