Question

Two vessels A and B contain spirit and water in the ratio 2 : 7 and 5: 4 respectively. Their contents are mixed in the ratio of 1 : 2. What is the ratio of spirit and water in the new mixture?
1. 7 : 4
2. 7 : 5
3. 2 : 5
4. 4 : 5

Answer 1

Correct Answer - Option 4 : 4 : 5

Given:

First vessel A contain spirit and water in the ratio 2 : 7

Second vessels B contain spirit and water in the ratio 5: 4 

Calculation:

Let x letre of first mixture and 2x of second mixture is taken of,

As we know that if an amount of mixture is taken of then it is also in same ratio.

According to the question:

Spirit = (x × 2/9) = 2x/9 in first mixture

Water = (x × 7/9) = 7x/9 in first mixture

Spirit = (2x × 5/9) = 10x/9 in second mixture

Water = (2x × 4/9) = 8x/9 in second mixture

Now,

Total sprit = 2x/9 + 10x/9 = 12x/9

Total water = 7x/9 + 8x/9 = 15x/9

Ratio of spirit and water = 12x/9 : 15x/9 = 4 : 5

∴ The ratio of spirit and water in the new mixture is 4 : 5.