Three containers are filled with a mixture of sugar and water. The ratio of their quantity is 5:4:3. The ratio of sugar and water in those containers is 2:3, 4:5, and1:3 respectively. These containers are then mixed and shifted to another container. Now, find the ratio of sugar and water in the mixture.

Given:

Ratio of quantity of 3 containers = 5 : 4 : 3

Ratio of sugar and water in first container = 2 : 3

Ratio of sugar and water in second container = 4 : 5

Ratio of sugar and water in third container = 1 : 3

Calculation:

Let the quantity of container 1, 2 and 3 is 5x, 4x, and 3x respectively

Now, in container-1 with volume 5x,

Quantity of sugar = 2/5 × 5x = 2x

Quantity of water = 3/5 × 5x = 3x

Similarly, in container-2 with volume 4x,

Quantity of sugar = 4/9 × 4x = 16x/9

Quantity of water = 5/9 × 4x = 20x/9

And, in container-3, with volume 3x,

Quantity of sugar = 1/4 × 3x = 3x/4

Quantity of water = 3/4 × 3x = 9x/4

Now in container 4,

Total sugar = 2x + 16x/9 + 3x/4

⇒ (72x + 64x + 27x)/36

⇒ 163x/36

Total water = 3x + 20x/9 + 9x/4

⇒ (108x + 80x + 81x)/36

⇒ 269x/36

The ratio of sugar and water = 163x/36 : 269x/36

⇒ 163 : 269

∴ The ratio of milk and water in the container is 163 : 269

Shortcut Trick