Question

Two solutions A and B contain spirit and water in the ratio 5:6 and 7: 4. respectively. They are mixed in the
ratio 3 : 5 in a vessel In 220 ml of the solution in the vessel how much water (in ml) should be added to
make it a solution in which the ratio of spirit and water is 25 : 27 ?
0 45
O 50
0 40
O 35​

Answer 1

40 is the correct answer

Answer 2

Solution :-

→ Solution A has spirit : water = 5 : 6

→ Solution B has spirit : water = 7 : 4

→ Mixed in the ratio = 3 : 5

So,

→ In mixture total spirit = [(3/8) * (5/11) + (5/8) * (7/11)] = [(15/88) + (35/88)] = (50/88) = (25/44)

→ In mixture total water = [(3/8) * (6/11) + (5/8) * (4/11)] = [(18/88) + (20/88)] = (38/88) = (19/44)

then,

→ In 220 ml of the solution total spirit = 220 * (25/44) = 125 ml

→ In 220 ml of the solution total water = 220 * (19/44) = 95 ml

Now, let us assume that, x ml of water is added and ratio of spirit and water becomes 25 : 27 .

therefore,

→ 125/(95 + x) = 25/27

→ 125 * 27 = 25(95 + x)

→ 5 * 27 = 95 + x

→ 135 = 95 + x

→ x = 135 - 95

→ x = 40 ml (Ans. C)

Hence, 40 ml of water should be added to make it a solution in which the ratio of spirit and water is 25 : 27 .

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