Three girls x, y and z were paid in the ratio 4 : 5 : 6 , respectively for doing a job. If the difference between the maximum amount and the minimum amount got by any two of them is Rs. 300, then what is the total amount got by x and z for doing the job?

Option 1 -

Rs. 1500

Option 2 -

Rs. 1500

Option 3 -

Rs. 2250

Option 4 -

Rs. 1550

2 Views | Posted a month ago

Asked by Shiksha User

1 Answer

Answered by

Raj Pandey | Contributor-Level 9

a month ago

Correct Option - 1

Detailed Solution:

It is given that they were paid in the ratio 4 : 5 : 6 s for doing the job.

So, maximum amount would have been got by z and the minimum amount obtained by x.

Amount obtained by x = $\frac{}{}$ $= 4 \times \frac{T}{15}$

where T is the total amount that all of them got together.

Amount obtained by z $= 6 \times \frac{T}{15}$ $\frac{}{}$

Now as per the problem,

$= 6 \times \frac{T}{15} - 4 \times \frac{T}{15} = 300$

$= 2 \times \frac{T}{15} = 300$

T = Rs. 2250

Share of x and z $= 6 \times \frac{T}{15} + 4 \times \frac{T}{15} = 10 \times \frac{T}{15} =$ $\frac{}{} \frac{}{} \frac{}{}$ Rs. 1500

It is given that they were paid in the ratio 4 : 5 : 6 s for doing the job.So, maximum amount would have been got by z and the minimum amount obtained by x.Amount obtained by x = <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math> <math> <mrow> <mo>=</mo> <mn>4</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </math> where T is the total amount that all of them got together.Amount obtained by z   <math> <mrow> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> </mrow> </math> <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math>Now as per the problem, <math> <mrow> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>−</mo> <mn>4</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> <math> <mrow> <mo>=</mo> <mn>2</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mn>3</mn> <mn>0</mn> <mn>0</mn> </mrow> </math> T = Rs. 2250Share of x and z <math> <mrow> <mo>=</mo> <mn>6</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>+</mo> <mn>4</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> <mn>1</mn> <mn>0</mn> <mo>×</mo> <mfrac> <mrow> <mi>T</mi> </mrow> <mrow> <mn>1</mn> <mn>5</mn> </mrow> </mfrac> <mo>=</mo> </mrow> </math> <math><mrow><mfrac><mrow></mrow><mrow></mrow></mfrac><mfrac><mrow></mrow><mrow></mrow></mfrac><mfrac><mrow></mrow><mrow></mrow></mfrac></mrow></math> Rs. 1500

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Three girls x, y and z were paid in the ratio 4 : 5 : 6 , respectively for doing a job. If the difference between the maximum amount and the minimum amount got by any two of them is Rs. 300, then what is the total amount got by x and z for doing the job?

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