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 average number of red balls in B, D and E.

The correct answer is 389.

To find the average number of red balls in bags B, D, and E, we first need to determine the total number of balls and the number of red balls in each of these bags.

Let the total number of balls in any bag be $T$, the percentage of red balls be $r\%$, and the percentage of blue balls be $(100-r)\%$.

Since the percentage of red balls in all bags is greater than 50%, the number of red balls is greater than the number of blue balls. Therefore, the difference between red and blue balls can be expressed as:
$\text{Difference}=(r\%-(100-r)\%)\times T=(2r-100)\%\times T$

1. For Bag B:
Percentage of red balls, $r_B=66.5\%$
Difference between red and blue balls = 198
Using the formula:
$(2\times 66.5-100)\%\times T_B=198$
$33\%\times T_B=198$
$T_B=\frac{198\times 100}{33}=600$
Number of red balls in Bag B ($R_B$):
$R_B=66.5\%\times 600=399$

2. For Bag D:
Percentage of red balls, $r_D=60\%$
Difference between red and blue balls = 76
Using the formula:
$(2\times 60-100)\%\times T_D=76$
$20\%\times T_D=76$
$T_D=\frac{76\times 100}{20}=380$
Number of red balls in Bag D ($R_D$):
$R_D=60\%\times 380=228$

3. For Bag E:
Percentage of red balls, $r_E=72\%$
Difference between red and blue balls = 330
Using the formula:
$(2\times 72-100)\%\times T_E=330$
$44\%\times T_E=330$
$T_E=\frac{330\times 100}{44}=750$
Number of red balls in Bag E ($R_E$):
$R_E=72\%\times 750=540$

Average Number of Red Balls in B, D, and E:
$\text{Average}=\frac{R_B+R_D+R_E}{3}$
$\text{Average}=\frac{399+228+540}{3}$
$\text{Average}=\frac{1167}{3}=389$