# If 50 litres of milk costs Rs 1675, what is the cost of $35\dfrac{1}{2}$ litres of milk?

Answer

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**Hint:**To find the cost of $35\dfrac{1}{2}$ litres of milk, we will use the unitary method. Using this method, we can find the cost of 1 litre of milk by dividing Rs 1675 by 50. Then, we can find the cost of $35\dfrac{1}{2}$ litres of milk by multiplying the cost of 1 litre of milk with $35\dfrac{1}{2}$ .

**Complete step by step solution:**

We have to find the cost of $35\dfrac{1}{2}$ litres of milk. Let us find the cost of 1 litres of milk using the unitary method. We are given that 50 litres of milk costs Rs 1675.

$\Rightarrow 50\text{L}=\text{Rs}.1675$

Therefore, the cost of 1 litre of milk can be found by dividing 1675 by 50.

$\Rightarrow 1\text{L}=\text{Rs}\dfrac{1675}{50}$

Now, we have to find the cost of $35\dfrac{1}{2}$ . For this, we have to multiply the cost of 1 litre of milk by $35\dfrac{1}{2}$ .

\[\Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times 35\dfrac{1}{2}\]

Let us convert the mixed fraction $35\dfrac{1}{2}$ into fractional form. We know that a mixed fraction of the form $Q\dfrac{R}{d}$ is converted into its fractional form by $\dfrac{Q\times d+R}{d}$ . Therefore, we can write $35\dfrac{1}{2}$ as

\[\begin{align}

& \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{35\times 2+1}{2} \\

& \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{70+1}{2} \\

& \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{1675}{50}\times \dfrac{71}{2} \\

\end{align}\]

Let us cancel the common factor 25 from the numerator and the denominator.

\[\Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{{{\require{cancel}\cancel{1675}}^{67}}}{{{\require{cancel}\cancel{50}}^{2}}}\times \dfrac{71}{2}\]

We can write the result of above simplification as

\[\begin{align}

& \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{67}{2}\times \dfrac{71}{2} \\

& \Rightarrow 35\dfrac{1}{2}\text{L}=\dfrac{4757}{4} \\

\end{align}\]

Now, we have to divide 4757 by 4.

\[\Rightarrow 35\dfrac{1}{2}\text{L}=\text{Rs }1189.25\]

Hence, the cost of $35\dfrac{1}{2}$ litres of milk is Rs 1189.25.

**Note:**Students have a chance of making mistakes when applying unitary methods. They may find the cost of 1 litre of milk by multiplying Rs 1675 by 50 which leads to wrong result. Students must never forget to write the units at the end.

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