Three solutions having ethanol and methanol in the ratio 1 : 2, 2 : 3 and 3 : 4 are mixed in the ratio 2 : 4 :1 . Find the ratio of ethanol and methanol in the resultant mixture.

Option 1 -

283 : 452

Option 2 -

452 : 283

Option 3 -

226 : 283

Option 4 -

None of these

2 Views | Posted a month ago

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1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 1

Detailed Solution:

Let the solutions added be 2, 4 and 1 litre, respectively. Then quantity of ethanol in the solution is

$2 \times \frac{1}{3} + 4 \times \frac{2}{5} + 1 \times \frac{3}{7}$

$\begin{array}{l} = \frac{2}{3} + \frac{8}{5} + \frac{3}{7} \\ = \frac{70 + 168 + 45}{105} \\ = \frac{283}{105} \end{array}$

So, the quantity of methanol

$\begin{array}{l} = 7 - \frac{283}{105} \\ = \frac{735 - 283}{105} \\ = \frac{452}{105} \end{array}$

So the ratio of ethanol to methanol in the resultant solution is 283: 452.

Let the solutions added be 2, 4 and 1 litre, respectively. Then quantity of ethanol in the solution is <math> <mrow> <mn>2</mn> <mo>×</mo> <mfrac> <mrow> <mn>1</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> <mo>+</mo> <mn>1</mn> <mo>×</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> </math> <math> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>8</mn> </mrow> <mrow> <mn>5</mn> </mrow> </mfrac> <mo>+</mo> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>7</mn> <mn>0</mn> <mo>+</mo> <mn>1</mn> <mn>6</mn> <mn>8</mn> <mo>+</mo> <mn>4</mn> <mn>5</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>2</mn> <mn>8</mn> <mn>3</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </math> So, the quantity of methanol <math> <mtable columnalign="left"> <mtr> <mtd> <mrow> <mo>=</mo> <mn>7</mn> <mo>−</mo> <mfrac> <mrow> <mn>2</mn> <mn>8</mn> <mn>3</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>7</mn> <mn>3</mn> <mn>5</mn> <mo>−</mo> <mn>2</mn> <mn>8</mn> <mn>3</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>=</mo> <mfrac> <mrow> <mn>4</mn> <mn>5</mn> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </mtd> </mtr> </mtable> </math> So the ratio of ethanol to methanol in the resultant solution is 283: 452.

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Three solutions having ethanol and methanol in the ratio 1 : 2, 2 : 3 and 3 : 4 are mixed in the ratio 2 : 4 :1 . Find the ratio of ethanol and methanol in the resultant mixture.

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