[0:00]A vessel contains a mixture of milk and water in the respective ratio of 10:3. Twenty-six liters of this mixture was taken out and replaced with 10 liters of water. If the respective ratio of milk and water in the resultant mixture was 5:2, what was the initial quantity of mixture in the vessel? (in liters) Now, in here we are given that the ratio of milk and water is 10:3. So the ratio of milk and water is 10:3. Now let's say, there is 10x milk and 3x water. Twenty-six liters of this mixture was taken out. Now this 26 liter that has been taken out will be taken out in the same ratio of 10:3, right? So that means how much milk is taken out? Milk is taken out this 10 parts out of the total 13 parts, so the milk that is taken out is 10 parts out of the total 13 parts from this 26 liters, so 13 * 1 = 13 * 2. So 20 liters of milk is taken out. Let's find out how much water is taken out. Water that is taken out is three parts from this total 13 parts. The water that is taken out is three parts from this total 13 parts of 26 liters. So 13 * 2, 3 * 2 = 6 liters.
[1:16]So 20 liters of milk is taken out, 6 liters of water is taken out. So from this 10x, 20 liters of milk is taken out and from this 3x water, 6 liters of water is taken out. Going further, and replaced with 10 liters of water. Now the quantity of milk remains the same, but we are adding water here, 10 liters of water, so we add 10 here. So we get 10x - 20 of milk and 3x - 6 + 10 + 4 water. If the respective ratio of milk and water in the resultant mixture was 5:2. Now, this is the resultant mixture, right? This is the ratio of the resultant mixture and this ratio is given to us as 5:2, all right? So this ratio is same as this ratio, which is 5:2. So I can write it as 10x - 20 upon 3x + 4 = 5 / 2. Right? Now let's take this two on the left hand side, so we get 2 * 10 = 20x, 20 * 2 = 40 = 5 * 3 = 15x, 5 * 4 = 20. 20x - 15x will give me 5x = 20 + this 40 will give me 60. 5 * 1 = 5 * 2 = 10. So we have got the value of x, which is 12. What are we asked? We are asked what was the initial quantity of mixture in the vessel. So initial quantity of mixture was 10x milk was there and 3x water was there. So total quantity in the initial mixture was 10x milk + 3x water. So total is 13x. x is 12. So 13 * 12. This will give me 156 and this is our required answer. Here option D is the correct one.
