If a man sells a pen at 24% profit and pencil at 54% profit, he earns Rs. 1960.2 as profit. But if he sells the pen at 11\(\frac{1}{9}\)% and pencil at 14\(\frac{2}{4}\)% loss then he bears no profit no loss. Find the cost price of the pencil and the pen.

2310, 2970

pen × 11\(\frac{1}{9}\)% profit = pencil × 14\(\frac{2}{7}\)% loss

  ratio of                   Pen         :      Pencil

                                 14\(\frac{2}{7}\)%     :          11\(\frac{1}{9}\)

                                   \(\frac{1}{7}\)          :           \(\frac{1}{9}\)

CP                               9         :          7

 Let Make this ratio       900      :       700

pen at 24% profit = 900R × \(\frac{24}{100}\)   = 216R

pencil at 54% profit = 700R × \(\frac{54}{100}\) = 378R

According to question , 216R + 378R =  1960.2

594R = 1960.2

1R = 3.3

Cost price of pen = 900 × 3.3 = 2970

Cost price of pencil = 700 × 3.3 = 2310

Hence, cost price of pencil and pen is 2310 and 2970 respectively.