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.
a) 150 liters
b) 175 liters
c) 120 liters
d) 180 liters
e) None of these
Sol:
Initial quantity of wine in the vessel = 8x
Initial quantity of water in the vessel = 7x
(8x – 45 * 8/15 + 8x * 7/20)/(7x – 45 * 7/15 + 23)
= 7/6
(8x – 24 + 14x/5)/(7x – 21 + 23) = 7/6
((40x – 120 + 14x)/5)/(7x + 2) = 7/6
(54x – 120)/(35x + 10) = 7/6
324x – 720 = 245x + 70
79x = 790
x = 10 liters
Initial quantity of mixture in the vessel = 8 * 10 +
7 * 10 = 150 liters
