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Algebra
Level
pending
Mayank and Gaurav have the same number of marbles when they started playing. After some time Mayank gains 20 marbles and later he loses 2/3rd of what he had now Gaurav has 4 times as many marbles as Mayank has. What are the initial number of marbles that each of them had?
The answer is 100.
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1 solution
Let each of them have "x" marbles initially.
After Mayank gains 20 marbles he has (x+20) while Gaurav has (x-20) marbles.
Mayank then loses 2/3 marbles. Therefore he now has 1/3 of his previous marbles= 1/3(x+20)
But Gaurav now has (x-20)+2/3(x+20) ...... [As he gains 2/3 marbles from Mayank]
=1/3(x-20)... [On solving]
Now Gaurav has 4 times the marbles of Mayank, therefore,
4[1/3(x+20)]=1/3(x-20)
On solving we get x=100. Therefore each one had 100 marbles at the beginning.
You can verify that also.