Question

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

Answer 1

Let number of pens = x
                    pencils = y

x+y=40   <<<<<<<<<<< eqn(1)

(x+5) = 4(y-5)   
⇒ x+5 = 4y - 20
⇒ x = 4y -25

Putting in eqn(1)
 x+y=40
⇒4y-25+y = 40
⇒5y = 40+25
⇒5y = 65
⇒ y = 65/5 = 13

x = 40-13=27

No. of pencils = 27
No.of pens = 13

Answer 2

Let us say Reena has P number of pens and N number of pencils.

As the total number is 40 ,      P + N = 40
                                          N = 40 - P      ---- equation 1

If she has 5 more pencils, it means number of pencils = N + 5
If she has 5 less pens, it means number of pens = P - 5

Then number of pencils becomes 4 times the number of pens.  That is,
        N + 5 =  4 * (P - 5)
  so   N + 5  =  4 P - 4 * 5 = 4 P - 20
  so    N = 4 P - 25     

Substitute N = 40 -P from equation 1,
         N = 40 - P = 4 P  - 25

              40 + 25 = 4 P + P                or                     65 = 5 P

                 P = 13
     from equation 1,   N = 40 - P = 27

She has 27 pencils and 13 pens.