Proportional Reasoning - 2 | IT

Question 1

Viswanath made idlis by mixing 6 cups of rice with 3 cups of urad dal, while Puneet made idlis by mixing 4 cups of rice with 2 cups of urad dal. If cooked in the same way, would their idlis taste the same?

Solution

Understand the Question

The taste of the idlis depends on the proportion (ratio) of rice to urad dal in the batter, not on the total quantity made.
If both Viswanath and Puneet use the same ratio of rice to urad dal, their idlis will taste the same.
We calculate and compare the ratio of $\text{rice} : \text{urad dal}$ for both preparations.

Step 1 · Calculate Viswanath's Ratio

For Viswanath:

\begin{aligned} \text{Ratio}_{\text{Viswanath}} &= \dfrac{\text{Cups of rice}}{\text{Cups of urad dal}} \\[0.6em] &= \dfrac{6}{3} \\[0.6em] &= 2 \end{aligned}

This means Viswanath uses $2$ parts rice for every $1$ part urad dal ( $2 : 1$ ).

Step 2 · Calculate Puneet's Ratio

For Puneet:

\begin{aligned} \text{Ratio}_{\text{Puneet}} &= \dfrac{\text{Cups of rice}}{\text{Cups of urad dal}} \\[0.6em] &= \dfrac{4}{2} \\[0.6em] &= 2 \end{aligned}

This means Puneet also uses $2$ parts rice for every $1$ part urad dal ( $2 : 1$ ).

Step 3 · Compare the Ratios

Comparing the two ratios: $\text{Ratio}_{\text{Viswanath}} = \text{Ratio}_{\text{Puneet}} = 2$

Since the ratios of rice to urad dal are equal ( $2 : 1$ ), their idlis will taste the same.

Answer

Yes, their idlis would taste the same.

Common Mistakes

Comparing Absolute Quantities: Thinking Viswanath's idlis will taste different because he used more cups ( $6$ vs $4$ ) of rice. Taste depends on the ratio, not the absolute amount.
Inconsistent Ratios: Comparing $\dfrac{\text{rice}}{\text{dal}}$ for one person and $\dfrac{\text{dal}}{\text{rice}}$ for the other.

Question 1

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