Divide Rs. 12540 among A, B and C so that A may receive 3/7 of as much as B and C together and B may receive 2/9 of as much as A and C together. What is C’s share?

Option 1 -

2280

Option 2 -

3762

Option 3 -

6498

Option 4 -

7480

3 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Vishal Baghel | Contributor-Level 10

a month ago

Correct Option - 3

Detailed Solution:

(c): A + B + C = 12540 .… (1)

$A = \frac{3}{7} (B + C)$

$\frac{A}{B + C} = \frac{3}{7}$

So, A’s Share = $\frac{3}{10} \times 12540 = 3762$ $\frac{}{}$

$B = \frac{2}{9} (A + C)$

$\frac{B}{A + C} = \frac{2}{9}$

So, B’s Share = $\frac{2}{11} \times 12540 = 2280$

(c): A + B + C = 12540 .… (1) <math> <mrow> <mi>A</mi> <mtext> </mtext> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> <mo stretchy="false"> (</mo> <mi>B</mi> <mo>+</mo> <mi>C</mi> <mo stretchy="false">)</mo> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mi>A</mi> </mrow> <mrow> <mi>B</mi> <mo>+</mo> <mi>C</mi> </mrow> </mfrac> <mtext> </mtext> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>7</mn> </mrow> </mfrac> </mrow> </math> So, A’s Share = <math> <mrow> <mfrac> <mrow> <mn>3</mn> </mrow> <mrow> <mn>1</mn> <mn>0</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mn>2</mn> <mn>5</mn> <mn>4</mn> <mn>0</mn> <mo>=</mo> <mn>3</mn> <mn>7</mn> <mn>6</mn> <mn>2</mn> </mrow> </math> <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math> <math> <mrow> <mi>B</mi> <mtext> </mtext> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> <mtext> </mtext> <mtext> </mtext> <mo stretchy="false"> (</mo> <mi>A</mi> <mtext> </mtext> <mtext> </mtext> <mo>+</mo> <mtext> </mtext> <mtext> </mtext> <mi>C</mi> <mo stretchy="false">)</mo> </mrow> </math> <math> <mrow> <mfrac> <mrow> <mi>B</mi> </mrow> <mrow> <mi>A</mi> <mo>+</mo> <mi>C</mi> </mrow> </mfrac> <mtext> </mtext> <mo>=</mo> <mtext> </mtext> <mtext> </mtext> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>9</mn> </mrow> </mfrac> </mrow> </math> So, B’s Share = <math> <mrow> <mfrac> <mrow> <mn>2</mn> </mrow> <mrow> <mn>1</mn> <mn>1</mn> </mrow> </mfrac> <mo>×</mo> <mn>1</mn> <mn>2</mn> <mn>5</mn> <mn>4</mn> <mn>0</mn> <mo>=</mo> <mn>2</mn> <mn>2</mn> <mn>8</mn> <mn>0</mn> </mrow> </math>

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Divide Rs. 12540 among A, B and C so that A may receive 3/7 of as much as B and C together and B may receive 2/9 of as much as A and C together. What is C’s share?

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