Number of Pens and Pencils

Video Explanation

Question

Reena has pens and pencils which together are 40 in number. If she has 5 more pencils and 5 less pens, then number of pencils would become 4 times the number of pens. Find the original number of pens and pencils.

Solution

Step 1: Let the Variables

Let the number of pens = \(x\)

Let the number of pencils = \(y\)

Step 2: Form the Equations

Total number is 40:

\[ x + y = 40 \quad (1) \]

After change:

Pens = \(x – 5\)

Pencils = \(y + 5\)

Given condition:

\[ y + 5 = 4(x – 5) \quad (2) \]

Step 3: Simplify Equation (2)

\[ y + 5 = 4x – 20 \]

\[ y = 4x – 25 \quad (3) \]

Step 4: Substitute in Equation (1)

\[ x + (4x – 25) = 40 \]

\[ 5x – 25 = 40 \]

\[ 5x = 65 \]

\[ x = 13 \]

Step 5: Find the Value of y

\[ y = 40 – 13 \]

\[ y = 27 \]

Conclusion

Original number of pens:

\[ \boxed{13} \]

Original number of pencils:

\[ \boxed{27} \]