A number theory problem by Didarul Alam

The best way is to plug in a value, let's say the initial money = 50. Then, the man gets 30 and the woman gets 20 as per ration. Now, 50 doubled = 100 and if the man still should get 30, then the wife gets 70. Hence ratio is 30 : 70 or 3 : 7

The problem can also be solved using algebra.

Take the value of money initially shared be x

money initially received by the man $= \frac{3x}{5}$

Now, , when x is doubled, the value the man receives is $\frac{2xy}{z}$ , where $y$ is the part he receives and $z$ is the total parts of the ratio.

As he is to receive the same amount, $\frac{3x}{5} = \frac{2xy}{z}$ $\frac{3x}{5 \times 2x} = \frac {y}{z}$ $\frac{3}{10} = \frac{y}{z}$ Now, the ratio would be given by $y : z-y$

So, $10 - 3 = 7$

$\boxed{ 3 : 7}$