A certain product P3 is made of two ingredients P1 and P2 in the proportion of 2 : 5. The price of P1 is three times that of P2. The overall cost of P3 is Rs. 10.4 per kg including labour charges of Rs.1.6 per kg. Find the cost of P1 & P2 per kg ?

Option 1 -

14.4, 4.8

Option 2 -

16.8, 5.6

Option 3 -

9.6, 3.2

Option 4 -

11.4, 3.8

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 2

Detailed Solution:

Let the price of P2 per kg be Rs. X. Then the price of P1 per kg = Rs. 3X.

1 kg of P3 P3contains

$(\frac{2}{7}) \times 1, i.e., \frac{2}{7} kg of A and \frac{5}{7} kg of B$

Price of 1 kg of P3 = $(\frac{2}{7}) \times 3 X + (\frac{5}{7}) X = (\frac{11}{7}) X$ $\frac{}{} \frac{}{} \frac{}{}$

P2y the given condition,

$\begin{array}{l} \frac{11 X}{7} = 10.4 - 1.6 = Rs. 8.8 \\ \Rightarrow X = 8.8 \times (\frac{7}{11}) = 5.6 \end{array}$

Hence, the price of P1 per kg = 3X = 3 × 5.6 = Rs. 16.8

Price of P2 per KG = Rs5.6

Let the price of P2 per kg be Rs. X. Then the price of P1 per kg = Rs. 3X.1 kg of P3 P3contains <math> <mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mn>2</mn></mrow><mrow><mn>7</mn></mrow></mfrac></mrow><mo>)</mo></mrow><mtext> </mtext><mtext> </mtext><mo>×</mo><mtext> </mtext><mtext> </mtext><mn>1</mn><mo>,</mo><mtext> </mtext><mtext> </mtext>i.e.<mo>,</mo><mtext> </mtext><mtext> </mtext><mfrac><mrow><mn>2</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mtext> </mtext><mtext> </mtext>kg<mtext> </mtext><mtext> </mtext>of<mtext> </mtext><mtext> </mtext>A<mtext> </mtext><mtext> </mtext>and<mtext> </mtext><mtext> </mtext><mfrac><mrow><mn>5</mn></mrow><mrow><mn>7</mn></mrow></mfrac><mtext> </mtext><mtext> </mtext>kg<mtext> </mtext><mtext> </mtext>of<mtext> </mtext><mtext> </mtext><mi>B</mi></mrow> </math> Price of 1 kg of P3 = <math> <mrow> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <mtext> </mtext> <mtext> </mtext> <mn>3</mn> <mi>X</mi> <mtext> </mtext> <mtext> </mtext> <mo>+</mo> <mtext> </mtext> <mtext> </mtext> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>X</mi> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>1</mn> <mn>1</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mi>X</mi> </mrow> </math> <math><mrow><mrow><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></mrow><mrow><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></mrow><mrow><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></mrow></mrow></math>P2y the given condition, <math> <mtable columnalign="left"> <mtr> <mtd> <mrow><mfrac><mrow><mn>1</mn><mn>1</mn><mi>X</mi></mrow><mrow><mn>7</mn></mrow></mfrac><mtext> </mtext><mtext> </mtext><mo>=</mo><mtext> </mtext><mtext> </mtext><mn>1</mn><mn>0</mn><mo>.</mo><mn>4</mn><mtext> </mtext><mtext> </mtext><mo>−</mo><mtext> </mtext><mtext> </mtext><mn>1</mn><mo>.</mo><mn>6</mn><mtext> </mtext><mtext> </mtext><mo>=</mo><mtext> </mtext><mtext> </mtext>Rs.<mtext> </mtext><mtext> </mtext><mn>8</mn><mo>.</mo><mn>8</mn><mtext> </mtext></mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mtext> </mtext> <mo>⇒</mo> <mtext> </mtext> <mtext> </mtext> <mi>X</mi> <mtext> </mtext> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mn>8</mn> <mo>.</mo> <mn>8</mn> <mtext> </mtext> <mtext> </mtext> <mo>×</mo> <mtext> </mtext> <mtext> </mtext> <mrow> <mo>(</mo> <mrow> <mfrac> <mrow> <mn>7</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </mfrac> </mrow> <mo>)</mo> </mrow> <mtext> </mtext> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mn>5</mn> <mo>.</mo> <mn>6</mn> </mrow> </mtd> </mtr> </mtable> </math> Hence, the price of P1 per kg = 3X = 3 × 5.6 = Rs. 16.8Price of P2 per KG = Rs5.6

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A certain product P3 is made of two ingredients P1 and P2 in the proportion of 2 : 5. The price of P1 is three times that of P2. The overall cost of P3 is Rs. 10.4 per kg including labour charges of Rs.1.6 per kg. Find the cost of P1 & P2 per kg ?

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