A shopkeeper mixes three varities of sugar costing Rs. 40 per kg, Rs. 48 per kg. and Rs. 60 per kg. and sells the mixture at a profit of 20% at Rs. 60 per kg. How many kgs of second variety will be in the mixture if 2 kgs of the third variety is there in the mixture ?

Cost price of mixture = 60 / 1.20 = Rs. 50/kg (since sold at 20% profit). Using allegation: Let second variety be x kg. First variety (Rs. 40) and third variety (Rs. 60, 2 kg) mix to give Rs. 50. Ratio 40 : 60 = 10 : 10 = 1 : 1. So 2 kg of third variety needs 2 kg of first variety. Average of (40 and 60) is 50. Now allegation between average 50 (from 2+2=4kg) and second variety 48 to get 50: 50 is at 4:1 ratio from 48 and 50, so second variety = 4 × 1 = 4 kg. Wait, let me reconsider. (40×2 + 60×2)/(2+2) = 200/4 = 50. So 4 kg at Rs. 50. To maintain Rs. 50 when mixing with Rs. 48, we need ratio 48:50 = 2:2, meaning equal quantities. So 4 kg of Rs. 48 type.