Alligation or Mixture problems
A person covers a distance of 100 kms in 10 hours, partly by walking at 7 km/hr and rest by running at 12 km/hr. Find the distance covered in each part.
Average speed = (100 / 10) = 10 km/hr. Ratio of time taken at 7 km/hr to 12 km/hr = 2 : 3 Time taken at 7 km/hr = 2 (2 + 3) × 10 = 4 hrs. Distance covered at 7 km/hr = 7 × 4 = 28 km. Distance covered at 12 km/hr = 100 ? 28 = 72 km.
By the rule of alligation: Cost of 1 kg pulses of 1st kind Cost of 1 kg pulses of 2nd kind Rs. 15 Mean Price Rs. 16.50 Rs. 20 3.50 1.50 ∴ Required rate = 3.50 : 1.50 = 7 : 3.
Let the quantity of the wine in the cask originally be x litres Then, quantity of wine left in cask after 4 operations = x 1 - 8 x 4 litres ? x 1 - 8 x 4 x = 16 81 ? 1 - 8 x 4 = 2 3 4 ? x = 24
Total quantity of iron = 4 (1 / 4) + 6 (2 / 3) = 1 + 4 = 5 kg. Total quantity of tin = (4 + 6) ? 5 = 5 kg. In the resultant mixture, iron : tin = 5 : 5 or 1 : 1
EXAMIANS