In a mixture ratio of three liquids A, B and C is 4 : 3 : 5 respectively. From this mixture 24 litre mixture is taken out and replaced with liquid C hence new ratio of liquid A, B and C in mixture becomes 12 : 9 : 19. Find the initial quantity of mixture- एक मिश्रण में तीन द्रवों A, B तथा C का अनुपात क्रमशः 4 : 3 : 5 था। मिश्रण से 24 लीटर मिश्रण निकाल लिया गया तथा उसके स्थान पर द्रव C को मिला दिया गया अतः अब मिश्रण में द्रवA,B तथा C का नया अनुपात 12 : 9 : 19 हो गया। मिश्रण की प्रारम्भिक मात्रा ज्ञात कीजिए।

Let initial quantities be 4x, 3x, 5x for A, B, C respectively (total = 12x). When 24L is removed, the amounts removed maintain the ratio: 8L of A, 6L of B, 10L of C. After removal and adding 24L of C: New A = 4x-8, New B = 3x-6, New C = 5x-10+24 = 5x+14. Given new ratio is 12:9:19. Setting up: (4x-8)/12 = (3x-6)/9 = (5x+14)/19. From first two: 3(4x-8) = 4(3x-6), which gives 12x-24 = 12x-24 (identity, always true). Using first and third: 19(4x-8) = 12(5x+14), giving 76x-152 = 60x+168, so 16x = 320, x = 20. Initial mixture = 12x = 240L.