Profit and Loss - 02

Question:  A shopkeeper bought 30 kg of wheat at the rate of Rs 45 per kg. He sold 40% of the total quantity at the rate of Rs 50 per kg. Approximately, at what price per kg should he sell the remaining quantity to make 25% overall profit?  [Allahabad Bank PO, 2010]

(1) Rs.54     (2) Rs.52     (3) Rs.50   (4) Rs.60    (5) Rs 56

                Soln.          By method of Alligation

                     I (Rs/kg)                        II (Rs/kg)

                      50                                ? = 60.41=60 (approx) Ans.     

                                    Mean (Rs/kg)                    

                                      56.25

                      2 ≡ ?            :               3 ≡ 6.25

                So, 2 ≡  4.16                      1 ≡ 2.08 (approx.)

[Detailed Explanation: Ratio of quantities is 40% : 60% i. e., 2 : 3

40% of the quantities is sold at Rs 50/kg; while 60% of the quantities is sold at what percent? This is to be determined.

Overall profit (mean profit) is 25%, so mean selling price is 125% of Rs 45 = Rs 56.25

56.25 – 50 = 6.25,which is equivalent to 3,i.e. 1 ≡ 2.08 (approx.); so,  2 ≡ 4.16

? – 56.25 = 4.16 That is, ? = 60.41 ≡ 60 (approx.) Ans.]

By method of Alligation,

                     I (Rs/kg)                        II (Rs/kg)

                      50                                ? = 60.41=60 (approx) Ans.    

                                    Mean (Rs/kg)                   

                                      56.25

                      2 ≡ ?            :               3 ≡ 6.25

                So, 2 ≡  4.16                      1 ≡ 2.08 (approx.)