Two vessels `A` and `B` contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture in vessel `C` containing spirit and water in the ratio 8:5? `4\ :3` (b) `3\ :4` (c) `5\ :6` (d) `7\ :9`

Explanation

To solve the problem, we need to find the ratio in which the mixtures from vessels A and B should be mixed to obtain a new mixture in vessel C with a specified spirit-to-water ratio. Let's break down the solution step by step.

### Step 1: Understand the Ratios in Vessels A and B
- Vessel A contains spirit and water in the ratio of 5:2.
- Vessel B contains spirit and water in the ratio of 7:6.

### Step 2: Calculate the Proportion of Spirit in Each Vessel
- For vessel A:
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