Two vessels A and B contain spirit and water mixed in ratio 5 : 2 and 7 : 6 respectively. Find ratio in which se mixtures be mixed to obtain a new mixture in vessel C containing spirit and water in ratio 8 : 5 ?

Let the Cost price of spirit be Rs. 1 per litre
Spirit in 1 litre mixture in A = $$\frac{{5}}{{7}}$$ litre;
Cost price of 1 litre mixture in A = Rs. $$\frac{{5}}{{7}}$$
Spirit in 1 litre mixture of B = $$\frac{{7}}{{13}}$$ litre;
Cost price of 1 litre mixture in B = Rs. $$\frac{{7}}{{13}}$$
Spirit in 1 litre mixture of C = $$\frac{{8}}{{13}}$$ litre;
Mean price = Rs. $$\frac{{8}}{{13}}$$
By the rule of alligation, we have:

∴ Request ratio = $$\frac{{1}}{{13}}$$ : $$\frac{{9}}{{91}}$$ = 7 : 9