In what ratio must a person mix three kinds of rice costing him Rs 1.16,Rs 1.40 and Rs 1.72 per Kg so that the mixture may be worth Rs 1.37 per Kg?

Mix rice of first and third kind to get a mixture worth Rs 1.37 per Kg. C.P of 1 Kg rice of 1st kind 116p C.P of 1 Kg rice of 3rd kind 172p Mean Price 137p 1st kind             3rd kind 116                      172              137 35                        21 5             :            3  By Alligation rule: Quantity of 1st kind of rice/ Quantity of 3rd kind of rice = 5/3 So they must be mixed in the ratio 5:3 Mix rice of 1st kind and 2nd kind to obtain a mixture worth of Rs. 1.37per Kg 1st kind                     2nd kind    116                             140                 137 3                 :                 21 1                 :                  7   By alligation rule: Quantity of 1st kind of rice/Quantity of 2nd kind of rice = 1/7 So they must be mixed in the ratio 1:7 Thus, Quantity of 2nd kind of rice /Quantity of 3rd kind of rice = (Quantity of 1st kind of rice / Quantity of 3rd kind of rice) × (Quantity of 2nd kind of rice / Quantity of 1st kind of rice) ⇒ Quantity of 2nd kind of rice/ Quantity of 3rd kind of rice = (5/3 × 7/1) = 35:3  Thus, Quantities of wheat of 1st : 2nd : 3rd = 5:35:3