Question

Divide 50 pens in the ratio 4:5
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Answer 1

The pens can be divided into parts of 22 and 28 to have a ratio approximately of 4 : 5. ( Actual parts are 22.22 and 27.77)

Given :

The total number of pens = 50

To Find :

Pens in the ratio 4 : 5

Solution :

Ratio and Proportion :

• When the two quantities are in the ratio of "a:b", it denotes that Quantity 1 comprises "a" share out of the total parts and Quantity 2 comprises "b" share out of the total parts.
• There is a ratio constant "x" such that :

              $Qty1 : Qty2 = a : b\\Qty1 = a*x\\Qty2 = b*x$

• In this case, the total number of parts is: $(a+b)x$

Here the ratio of the two parts needs to be 4 : 5. Let us assume the ratio constant to be "x".

So, according to the above concepts :

• Part 1 count is : a * x = 4x
• Part 2 count is : b * x = 5x

The total count of the pens is given as 50. Equating that, we get :

             $4x + 5x = 50\\9x = 50\\x = 50/9$

Thus, we can find the count of individual quantities i.e. count in each part as :

• The quantity of Part 1 is 22.22 pens which is approximately 22.

                   $4x = 4(50/9)\\4x = 200/9\\4x = 22.22$

• The quantity of Part 2 is 27.77 pens which is approximately 28.

                    $5x = 5(50/9)\\5x = 250/9\\5x = 27.77$

Hence, the pens can be divided into groups of 22 and 28 to have a ratio approximately of 4 : 5.

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Answer 2

50 pens in the ratio 4:5 by allocating 22 pens to the first part and 27 pens to the second part.

To divide 50 pens in the ratio 4:5, we need to divide the total number of pens into parts that correspond to the ratio. In this case, the ratio is 4:5, which means that we need to divide the pens into two parts, with one part being four times smaller than the other part and the other part being five times larger than the smaller part.

To find the size of each part, we need to add the parts of the ratio, which in this case is 4+5 = 9. Next, we divide the total number of pens (50) by the sum of the parts of the ratio (9) to get the value of one part.

50/9 = 5.55

We then multiply this value by each part of the ratio to get the actual number of pens in each part.

4 x 5.55 = 22.22

5 x 5.55 = 27.75

Therefore, we can divide 50 pens in the ratio 4:5 by allocating 22 pens to the first part and 27 pens to the second part.

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