Mixtures and alligation
Commercial arithmetic · Mathematics
Study notes
Q: Mix Rs 60/kg sugar with Rs 40/kg sugar to get Rs 48/kg mixture. In what ratio? Step 1: Alligation: dearer d = 60, cheaper c = 40, mean m = 48. Step 2: Ratio = (d - m):(m - c) = (60 - 48):(48 - 40) = 12:8 = 3:2. Step 3: Mix 3 parts of Rs 60 sugar with 2 parts of Rs 40 sugar. Check: (3x60 + 2x40)/5 = 260/5 = 52... wait, recompute: (180+80)/5 = 260/5 = 52. Hmm, error! Correct: ratio of cheaper:dearer = (d-m):(m-c) = 12:8 means 12 parts cheaper? No: quantity of cheaper : dearer = (d - m):(m - c). So cheaper(40):dearer(60) = 12:8 = 3:2. Check: (3x40 + 2x60)/5 = (120+120)/5 = 240/5 = 48. Correct!