**Question: **

The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. If three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting solution has strength 20%. If instead the proportion is 3 : 2 : 1, then the resulting solution has strength 30%. A fourth solution, D, is produced by mixing B and C in the ratio 2 : 7. The ratio of the strength of D to that of A is

2 : 5 | |

1 : 3 | |

1 : 4 | |

3 : 10 |

**Show Answer**

Let 'a', 'b' and 'c' be the concentration of salt in Solutions A, B and C respectively.

It is given that three salt solutions A, B, C are mixed in the proportion 1 : 2 : 3, then the resulting Solution has strength 20%.

\( \Rightarrow \) \(\frac{{a + 2b + 3c}}{{1 + 2 + 3}} = 20\)

\( \Rightarrow \) \(a + 2b + 3c = 120\) ... (1)

Also, if the proportion is 3 : 2 : 1, then the resulting Solution has strength 30%.

\( \Rightarrow \) \(\frac{{3a + 2b + c}}{{1 + 2 + 3}} = 30\)

\( \Rightarrow \) \(3a + 2b + c = 180\) ... (2)

From equation (1) and (2), we get

\( \Rightarrow \) \(b + 2c = 45\)

By observation, we find that b = c = 15 and a = 45.

So if we mix Solution B and C in any ratio we get the mixture with 15% concentration whereas A's strength = 45%.

Hence, the required ratio = \(\frac{{15}}{{45}}\) = 1 : 3

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