A jar filled with water and milk in the ratio 7 : 9. 46 litres of mixture taken out and replaced with milk then ratio of water and milk become 6 : 11. Then find the initial quantity of mixture in the jar. एक जार में पानी और दूध का अनुपात 7: 9 है । 46 लीटर मिश्रण निकालकर दूध से बदल देने पर पानी और दूध का अनुपात 6 : 11 हो जाता है । तो जार में मिश्रण की प्रारंभिक मात्रा ज्ञात कीजिये ।

Let initial mixture be 16x (7x water + 9x milk). After removing 46L: water = 7x - (46/16x)×7x = 7x(1 - 23/8x), milk = 9x(1 - 23/8x). After adding 46L milk: water = 7x(1 - 23/8x), milk = 9x(1 - 23/8x) + 46. New ratio water:milk = 6:11. So 7x(1 - 23/8x) / [9x(1 - 23/8x) + 46] = 6/11. Solving: 77x(1 - 23/8x) = 54x(1 - 23/8x) + 276. Let x - 23/8 = k: 77xk = 54xk + 276, so 23xk = 276. Substituting k = (8x-23)/8: 23x(8x-23)/8 = 276. This gives 23x(8x-23) = 2208. Solving: 184x² - 529x - 2208 = 0, which gives x ≈ 14.875, so 16x ≈ 238.