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**Hint:**We are given a question of ratios. We will assume the numbers to be $x$ and $y$. And using the information given in the question, we will make equations in two variables and we will solve those equations to obtain the numbers. After finding both numbers, we will find the greater one out of them both and find the answer.

**Complete step by step answer:**

Assume that the numbers are $x$ and $y$. According to the question:

$\dfrac{x}{y}=\dfrac{3}{5}$

$\implies 5x=3y$

$\implies x=\dfrac{3}{5}y$

Now, we increase each of the numbers by 10. So the numbers now become $x+10$ and $y+10$. Then, according to the question:

$\dfrac{x+10}{y+10}=\dfrac{5}{7}$

$\implies 7\left(x+10\right)=5\left(y+10\right)$

$\implies 7x+70=5y+50$

$\implies 7x-5y+20=0$

Putting the value of $x$ as calculated above, we get:

$7\left(\dfrac{3}{5}y \right)-5y+20=0$

$21y-25y+100=0$

$\implies y=25$

Now to find the value of $x$, we put back the value of $y$. We get:

$x=\dfrac{3}{5}\times 25$

$\implies x=3\times 5=15$

Hence, the two numbers are 15 and 25. The bigger one out of the two is 25. Hence the greater number is 25.

**Note:**While putting the ratio, make sure that you don’t put it upside down. If $x$ and $y$ are in ratio 1:2 then $y=2x$ and not the other way round. Make sure that you don’t make many calculation mistakes while solving the ratio. Moreover, when the numbers are increased by 10 make sure that you add 10 to both $x$ and $y$.

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