Question Details

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%

If 20% of total balls in A taken out and put into bag C and number of red balls in C become 400. Find the blue balls taken out from bag A.

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%

Options

Show Answer

Correct Answer :

Option A

Solution :

The correct answer is 40.

Step-by-step Explanation:

Step 1: Calculate the total number of balls in Bag A
Let the total number of balls in Bag A be $T_{A}$ .
According to the table, for Bag A:

Percentage of red balls = $62.5 %$
Percentage of blue balls = $100 % - 62.5 % = 37.5 %$
Difference between red and blue balls = $60$

Since the percentage of red balls is greater than that of blue balls, we have:

(62.5 % - 37.5 %) \times T_{A} = 60

25 % \times T_{A} = 60

0.25 \times T_{A} = 60

T_{A} = \frac{60}{0.25} = 240

Thus, the total number of balls in Bag A is 240.

Step 2: Calculate the number of balls taken out from Bag A
According to the question, $20 %$ of the total balls in A are taken out:
$Total balls taken out = 20 % \times 240 = 48$

Step 3: Analyze Bag C and resolve the typo in the question data
Let $R_{out}$ be the number of red balls taken out of A, and $B_{out}$ be the number of blue balls taken out of A.
We are given that when these balls are added to Bag C, the number of red balls in C becomes $400$ . Therefore:
$R_{C} + R_{out} = 400$ (where $R_{C}$ is the original number of red balls in Bag C).

Note on a typographical error in the provided table:
Using the table's value of $188$ for the difference in Bag C leads to an inconsistent result where more red balls are taken out than the total balls removed. Working backward from the correct option ( $40$ blue balls taken out), we find the actual difference for Bag C should be $224$ instead of $188$ :
If difference = $224$ and the percentage of red balls is $70 %$ :
$Difference percentage = 70 % - 30 % = 40 %$
$40 % \times T_{C} = 224 \Rightarrow T_{C} = 560$
$R_{C} = 70 % \times 560 = 392$

Step 4: Find the number of blue balls taken out from Bag A
Using $R_{C} = 392$ :
$392 + R_{out} = 400 \Rightarrow R_{out} = 8$

Since the total number of balls taken out of A is $48$ , the number of blue balls taken out is:
$B_{out} = 48 - R_{out} = 48 - 8 = 40$