Question

Two vessels, A and B, contain spirit and water in the ratio 3: 4 and 5: 3, respectively. Find the ratio in which these two mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 4: 3.

• A. 3 : 8
• B. 3 : 7
• C. 5 : 8
• D. 4 : 7

Answer 1

Answer:

A. 3 : 8

Convert ratios to fraction of spirit:

• Vessel A (3:4) ⇒ Spirit = $( \frac{3}{7} )$

• Vessel B (5:3) ⇒ Spirit = $( \frac{5}{8} )$

• Required (4:3) ⇒ Spirit =$( \frac{4}{7} )$

  Apply alligation:

  $\text{Ratio} = (5/8 - 4/7) : (4/7 - 3/7)$
  $= \left(\frac{35 - 32}{56}\right) : \left(\frac{1}{7}\right)$
  $= \frac{3}{56} : \frac{1}{7}$
  

Convert:
$\frac{1}{7} = \frac{8}{56}$
So ratio:
$3 : 8$
Final Answer:

3 : 8