Answer:

i) ₹345

ii) 12.75 m

Step-by-step explanation:

Solution:-

Cost of 22.5m of cloth= ₹1350

Cost of 1m cloth = 1350/22.5

= ₹ 60

i) Cost of 5.75m of cloth = 5.75 × 60 = ₹345

ii) Length of cloth that can be buy in ₹1 = 1/60 m

Length of cloth that can be buy in ₹765 = 765 ×1/60

= 12.75 m

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Thanks for question

[tex]\large\underline{\sf{Solution-}}[/tex]

Given that,

22.5 m of cloth costs Rs 1350

We have to find the cost of 5.75 m of cloth and also, we have to find the how much we purchase for Rs 765

We know,

Direct variation :- Two variables x and y are said to be in direct variation iff, if x increases, then y increases or if x decreases, then y decreases.

So, here in this case, Less length, less is cost.

So, it means length and Cost are in Direct variation.

So,

[tex]\begin{array}{|c|c|c|c|c} \hline \rm Length \:( in \: m)&\rm 22.5&\rm 5.75&\rm y & \rm \\ \hline\rm Cost \: (in \: Rs)&\rm 1350&\rm x&\rm 765 & \rm \\ \hline \end{array} \\ [/tex]

So, using definition of direct variation

[tex]\rm \: \dfrac{22.5}{1350} = \dfrac{5.75}{x} = \dfrac{y}{765} \\ [/tex]

Taking first and second member

[tex]\rm \: \dfrac{22.5}{1350} = \dfrac{5.75}{x} \\ [/tex]

[tex]\rm \: 22.5 \times x = 1350 \times 5.75 \\ [/tex]

[tex]\rm \: x = \dfrac{1350 \times 5.75}{22.5} \\ [/tex]

[tex]\rm\implies \:x = 345 \: [/tex]

So, Cost of 5.75 m cloth us Rs 345

Now, Taking first and third member, we have

[tex]\rm \: \dfrac{22.5}{1350} = \dfrac{y}{765} \\ [/tex]

[tex]\rm \: 1350 \times y = 765 \times 22.5 \\ [/tex]

[tex]\rm \: y = \dfrac{765 \times 22.5}{1350} \\ [/tex]

[tex]\rm\implies \:y = 12.75 \\ [/tex]

Hence, 12.75 m of cloth can be purchased for Rs 765.

Hence,

[tex]\begin{array}{|c|c|c|c|c} \hline \rm Length \:( in \: m)&\rm 22.5&\rm 5.75&\rm 12.75 & \rm \\ \hline\rm Cost \: (in \: Rs)&\rm 1350&\rm 345&\rm 765 & \rm \\ \hline \end{array} \\ [/tex]