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A man mixes 5 kilolitres of milk at rs 6000 per kilolitre with 6 kilolitres at rs 5400 per kilolitre. How many kilolitres of water should be added to make the average value of the mixture rs 4800 per kilolitre? How many kilolitres of water has he added?
a) 2 kilolitre
b) 4 kilolitre
c) 3 kilolitre
d) 1.5 kilolitre

Respuesta :

Answer:

a) 2 kilolitres

Step-by-step explanation:

We can find the total of water should be added to make the average value of the mixture rs 4800/kilolitre using these following steps:

First, we find the total value and total volume of the milk mixture.

Given:

  • [tex]Volume_1[/tex] = 5 kilolitres
  • [tex]Rate_1[/tex] = rs 6000/kilolitre
  • [tex]Volume_2[/tex] = 6 kilolitres
  • [tex]Rate_2[/tex] = rs 5400 kilolitre

The formula for total value:

[tex]\boxed{Total\ Value=Volume\times Rate }[/tex]

Therefore:

[tex]Total\ Value_1=Volume_1\times Rate_1[/tex]

                     [tex]=5\times6000[/tex]

                     [tex]=rs\ 30000[/tex]

[tex]Total\ Value_2=Volume_2\times Rate_2[/tex]

                     [tex]=6\times5400[/tex]

                     [tex]=rs\ 32400[/tex]

[tex]Total\ Value\ of\ Mixture=Total\ Value_1+Total\ Value_2[/tex]

                                        [tex]=30000+32400[/tex]

                                        [tex]=rs\ 62400[/tex]

Second, we find the Volume of water added to make the new mixture have the Rate = rs 4800/kilolitre.

Let: [tex]Volume\ of\ water[/tex] = x kilolitres,

then:

  • [tex]Total\ Value\ of\ the\ New\ Mixture[/tex] = rs 62400
  • [tex]Total\ Volume\ of\ the\ New\ Mixture[/tex] = (5+6+x) = (11+x) kilolitres
  • [tex]Rate[/tex] = rs 4800/kilolitre

Therefore:

[tex]Total\ Value=Volume\times Rate[/tex]

[tex]62400=(11+x)\times 4800[/tex]

[tex]13=11+x[/tex]

[tex]\bf x=2\ kilolitres[/tex]

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