A vessel contains wine and water in the ratio of 8:7. 45 liters of mixture is removed and filled with 7\/20th of initial quantity of wine in the vessel and also 23 liters of water is added, then the ratio of the wine to water becomes 7:6. Find the initial quantity of mixture in the vessel.<\/p>\n\n\n\n
a) 150 liters<\/strong><\/p>\n\n\n\n b) 175 liters<\/p>\n\n\n\n c) 120 liters<\/p>\n\n\n\n d) 180 liters<\/p>\n\n\n\n e) None of these<\/p>\n\n\n\n Sol:<\/p>\n\n\n\n Initial quantity of wine in the vessel = 8x<\/p>\n\n\n\n Initial quantity of water in the vessel = 7x<\/p>\n\n\n\n (8x \u2013 45 * 8\/15 + 8x * 7\/20)\/(7x \u2013 45 * 7\/15 + 23)<\/p>\n\n\n\n = 7\/6<\/p>\n\n\n\n (8x \u2013 24 + 14x\/5)\/(7x \u2013 21 + 23) = 7\/6<\/p>\n\n\n\n ((40x \u2013 120 + 14x)\/5)\/(7x + 2) = 7\/6<\/p>\n\n\n\n (54x \u2013 120)\/(35x + 10) = 7\/6<\/p>\n\n\n\n 324x \u2013 720 = 245x + 70<\/p>\n\n\n\n 79x = 790<\/p>\n\n\n\n x = 10 liters<\/p>\n\n\n\n Initial quantity of mixture in the vessel = 8 * 10 +<\/p>\n\n\n\n 7 * 10 = 150 liters<\/p>\n","protected":false},"excerpt":{"rendered":" A vessel contains wine and water in the ratio of 8:7. 45 liters of mixture is removed and filled with 7\/20th of initial quantity of wine in the vessel and also 23 liters of water is added, then the ratio of the wine to water becomes 7:6. 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