The table given below shows the total number of red and blue balls in five different bags (A, B, C, D & E). it also shows the difference between red and blue balls and percentage of red balls with respect to total balls.

Total bags	Difference between red and blue balls	Percentage of red ball with respect to total balls
A	60	62.5%
B	198	66.5%
C	188	70%
D	76	60%
E	330	72%

Find the ratio of number of red balls in A and E together to number of blue balls in A.

The correct option is 23:3.

Let us find the number of red and blue balls in bag A and bag E step-by-step.

1. For Bag A:
Let the total number of balls in bag A be $T_A$.
The percentage of red balls is 62.5%.
Therefore, the percentage of blue balls is:
$100\%-62.5\%=37.5\%$
Since the percentage of red balls (62.5%) is greater than the percentage of blue balls (37.5%), there are more red balls than blue balls in bag A.
The difference between the percentages of red and blue balls is:
$62.5\%-37.5\%=25\%$ of the total balls.
We are given that the difference between red and blue balls in bag A is 60.
So, $25\%$ of $T_A=60$.
Thus, the total number of balls in bag A is:
$T_A=\frac{60}{0.25}=240$

Now, we can find the number of red and blue balls in bag A:
Number of red balls in A:
${\mathrm{Red}}_A=62.5\%of240=0.625\times 240=150$
Number of blue balls in A:
${\mathrm{Blue}}_A=240-150=90$

2. For Bag E:
Let the total number of balls in bag E be $T_E$.
The percentage of red balls is 72%.
Therefore, the percentage of blue balls is:
$100\%-72\%=28\%$
Since the percentage of red balls (72%) is greater than the percentage of blue balls (28%), there are more red balls than blue balls in bag E.
The difference between the percentages of red and blue balls is:
$72\%-28\%=44\%$ of the total balls.
We are given that the difference between red and blue balls in bag E is 330.
So, $44\%$ of $T_E=330$.
Thus, the total number of balls in bag E is:
$T_E=\frac{330}{0.44}=750$

Now, we can find the number of red balls in bag E:
${\mathrm{Red}}_E=72\%of750=0.72\times 750=540$

3. Find the required ratio:
We need to find the ratio of the number of red balls in A and E together to the number of blue balls in A.
Sum of red balls in A and E together:
${\mathrm{Red}}_A+{\mathrm{Red}}_E=150+540=690$
Number of blue balls in A:
${\mathrm{Blue}}_A=90$

The required ratio is:
$\frac{690}{90}=\frac{69}{9}=\frac{23}{3}$

Therefore, the ratio of the number of red balls in A and E together to the number of blue balls in A is 23:3.