Question

There are three types of liquid in a mixture of
700 cc. The ratio of the volumes of the first and
the second liquid is 2: 3 and that of the second
and the third is 4:5. 200 cc of the third liquid is
mixed with the mixture. Find the ratio of the
first and the third liquid in that final mixture.

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Answer 1

22 : 13

Step-by-step explanation:

First : Second = 2: 3

multiplying by 4 both sides

First : Second = 8 : 12

Second : Third = 4:5

multiplying by 3 both sides

Second : Third = 12 : 15

as now 12 is common for second in both ratios

=> First : Second : Third = 8 : 12 : 15

Let say quantities are

8A , 12A & 15A

total = 8A + 12A + 15A = 35A

=> 35A = 700

=> A = 20

First = 8A = 160 Litre

Second = 12A = 240 Litre

Third = 15A = 300 Litre

Let say A & B are mixed X & Y litre respectively

then

First = 160 + X litre

Second = 240 + Y Litre

Third = 300 Litre

Total = 700 + X + Y litre

New ratio

6 : 5 : 3

160 + X : 240 + Y : 300

(160 + X)/300 = 6/3

=> 160 + X = 600

=> X = 440

(240 + Y)/300 = 5/3

=> 240 + Y = 500

=> Y = 260

X : Y :: 440 : 260

=> X : Y :: 22 : 13

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