Ramesh gave 1/2 of his marbles to Samyak and 1/3 of what was left to ranchit. If ranchit gets 10 marbles how many did samyak get?
(1/3)x * (1/2)x = 10
1/6x = 10
x = 10/(1/6)
x = 10 * 6
x = ?
To find out how many marbles Samyak got, we need to first determine how many marbles Ramesh had initially.
Let's assume that Ramesh initially had 'x' marbles.
According to the given information, Ramesh gave 1/2 of his marbles to Samyak. Therefore, the number of marbles he gave to Samyak is (1/2)*x.
After giving away the marbles to Samyak, Ramesh is left with (x - (1/2)*x) = (1/2)*x marbles.
Then, Ramesh gave 1/3 of what was left to Ranchit. According to the given information, Ranchit got 10 marbles. Therefore, (1/3)*[(1/2)*x] = 10.
Simplifying the equation, we get (1/6)*x = 10.
To find the value of 'x', we can multiply both sides of the equation by 6:
(1/6)*x * 6 = 10 * 6
x = 60
So, Ramesh initially had 60 marbles.
Now, to find out how many marbles Samyak got, we can substitute 'x' into the equation for the number of marbles Ramesh gave to Samyak:
(1/2)*x = (1/2)*60 = 30
Therefore, Samyak got 30 marbles.