An algebra problem by Vishnu Kadiri

Algebra Level 3

Raj has two identical jugs, both completely filled with mixtures of mango pulp and milk. The ratio of mango pulp to milk in the first jug is 1 : 4 and in the second one it is 1: 3.

Raj now pours the mixtures from both jugs into a large jar. The ratio of mango pulp to milk in this container is

1:7 9:31 7:12 2:7

1 solution

Chew-Seong Cheong
Jul 29, 2015

Let the volume of the jug be $1$ , then the volumes of mango pulp $V_p$ and milk $V_m$ are as follows:

$\begin{cases} \text{Jug 1:} \Rightarrow \begin{cases} V_{p1} = \frac{1}{5} \\ V_{m1} = \frac{4}{5} \end{cases} \\ \text{Jug 2:} \Rightarrow \begin{cases} V_{p2} = \frac{1}{4} \\ V_{m2} = \frac{3}{4} \end{cases} \end{cases} \Rightarrow \begin{aligned} \color{#3D99F6}{V_{p1} + V_{p2}} : \color{#D61F06}{V_{m1} + V_{m2}} & = \color{#3D99F6}{\frac{1}{5} + \frac{1}{4}} : \color{#D61F06}{\frac{4}{5} + \frac{3}{4}} \\ & = \color{#3D99F6}{\frac{9}{20}} : \color{#D61F06}{\frac{31}{20}} \\ & = \boxed{9:31} \end{aligned}$

An algebra problem by Vishnu Kadiri

1 solution

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