Let's solve this problem step by step.
Let's say the initial number of red pens is 3x and the initial number of blue pens is 4x, where x is a positive integer.
According to the given information, the ratio of the number of red pens to the number of blue pens is 3:4. So, we have the equation:
(3x)/(4x) = 3/4
Cross-multiplying:
3 * 4x = 3x * 4
12x = 12x
This equation is true, so any value of x would work. Since we need to find the final number of red and blue pens, we can choose any value for x.
Let's assume x = 1.
So, initially, there are:
Red pens = 3 * 1 = 3
Blue pens = 4 * 1 = 4
Now, Mr. Lim puts another 20 pens into the box, so the total number of pens becomes:
Total pens = 3 + 4 + 20 = 27
According to the newly formed ratio, the number of red pens to the number of blue pens is 2:1. So, we have the equation:
(number of red pens)/(number of blue pens) = 2/1
Let's assume the number of red pens is 2y and the number of blue pens is y (where y is a positive integer).
So, we have the equation:
(2y)/(y) = 2/1
Cross-multiplying:
2 * y = 1 * 2y
2y = 2y
This equation is true, so any value of y would work. Since we need to find the final number of red and blue pens, we can choose any value for y.
Let's assume y = 1.
So, in the end:
Number of red pens = 2 * y = 2 * 1 = 2
Number of blue pens = y = 1
Therefore, in the end:
(A) There are 2 red pens.
(B) There is 1 blue pen.