Vessels A and B contain mixtures of milk and water in the ratios 4: 5and 5: 1respectively. In what ratio should quantities of the mixture be taken from A and B to form a mixture in which milk to water is in the ratio 5: 4?

05:02

Ratio of                         Milk      water

A                                    4     :     5

B                                    5     :     1

In mixture of A and B       5     :     4

Let us consider that In mixture quantities are taken from A and B in ratio = a : b

ATQ,

\(\frac{4a/(4 +5) + 5b/(5+1) }{5a/(4 +5) + 1b/(5+1)}\) = \(\frac{5}{4}\)

\(\frac{4a/9 + 5b/6 }{5a/9 + 1b/6 }\) = \(\frac{5}{4}\)

4 × [ \(\frac{4a}{9}\) + \(\frac{5b}{6}\) ] = 5 × [ \(\frac{5a}{9}\) + \(\frac{1b}{6}\) ]

4 × \(\frac{8a + 15b}{18}\) = 5 × \(\frac{10a + 3b}{18}\)

4 × \(\frac{8a + 15b}{18}\) = 5 × \(\frac{10a + 3b}{18}\)

32a + 60b = 50a + 15b

45b = 18a

\(\frac{a}{b}\) = \(\frac{45}{18}\)

\(\frac{a}{b}\) = \(\frac{5}{2}\)

So, In mixture quantities are taken from A and B in ratio = 5 : 2