Question

A tailor bought a number of suits at a cost of sh.57,000 from Ken-suit wholesalers. Had he bought the same number of suits from Umoja wholesalers it would have costed him sh.480 less per suit. This would have enabled him to buy 4 extra suits for the same amount of money.

1. Find the number of suits the tailor bought. 
2. The tailor later sold each suit for sh.720 more than he had paid for it. Determine the percentage profit he made. 

Answer 1

1. Let the number of suits bought be x
   let the price of each suit be Y sh. (ken-suit)
   ∴ xy = 57,000
      y = 57000 ( price per suit at Ken-suit)
                x
   (x + 4)(57000 − 480) =57000(umoja)
                   x
   57000 − 480x + 228000 − 1920 = 57000
                                 x
   57000x − 480x² + 228000 − 1920x = 57000x
   −480x² − 1920x + 228000 = 0
   480x² + 1920x − 228000 = 0
     x² + 4x − 475 = 0
   Solve to get x = 19.88508   x= −23.885
                     x≈20               x≈−24 (ignore)
2. B.P = 57000 =sh. 2850
               20
   S.P = 2850 + 720 =Sh,. 3570
   % profit = ^p/_B.P × 100
     720 × 100
    2850
   =25.26%