Proportional Reasoning - 1 | A

Question 1

Take your favourite dish. Find out all the ingredients and their respective quantities needed to make the dish for your family. Suppose you are celebrating a festival and you want to invite 15 guests. Find out the quantities of the ingredients required to cook the same dish for them.

Solution

Understand the Question

To cook a dish for a larger group, we use direct proportion to scale ingredient quantities.
If a recipe serves a family of $4$ members and $15$ guests are invited, the total number of people becomes $4 + 15 = 19$ .
The scaling factor is the ratio of the total people to the original family members: $\dfrac{19}{4} = 4.75$ .
Multiplying each ingredient's quantity by this scaling factor gives the required amount for everyone.

Step 1 · List Ingredients for Family (4 Members)

Let the chosen dish be Paneer Butter Masala for a family of $4$ members. Diagram 1

Baseline quantities for $4$ people:

Paneer: $250\text{ g}$
Tomatoes: $300\text{ g}$
Onions: $200\text{ g}$
Cashews: $20\text{ g}$
Ginger-Garlic paste: $15\text{ g}$
Butter: $30\text{ g}$
Fresh Cream: $60\text{ ml}$
Red Chilli Powder: $5\text{ g}$
Turmeric Powder: $2.5\text{ g}$
Coriander Powder: $5\text{ g}$
Garam Masala: $5\text{ g}$
Salt: $5\text{ g}$
Oil: $30\text{ ml}$
Water: $120\text{ ml}$
Kasuri Methi: $2\text{ g}$

Step 2 · Calculate Total Servings and Scaling Factor

Let $N_F$ be the number of family members, $N_G$ be the number of guests, and $N_T$ be the total number of people.

\begin{aligned} N_F &= 4 \text{ people} \\ N_G &= 15 \text{ people} \\ N_T &= N_F + N_G \\ &= 4 + 15 \\ &= 19 \text{ people} \end{aligned}

Calculate the scaling factor $S$ :

\begin{aligned} S &= \dfrac{\text{Total people}}{\text{Family members}} \\[0.6em] &= \dfrac{N_T}{N_F} \\[0.6em] &= \dfrac{19}{4} \\[0.6em] &= 4.75 \end{aligned}

Step 3 · Calculate Scaled Ingredient Quantities

Multiply each original quantity $Q_O$ by the scaling factor $S = 4.75$ to find the new quantity $Q_N$ :

Paneer: $Q_N = 250\text{ g} \times 4.75 = 1187.5\text{ g}$
Tomatoes: $Q_N = 300\text{ g} \times 4.75 = 1425\text{ g}$
Onions: $Q_N = 200\text{ g} \times 4.75 = 950\text{ g}$
Cashews: $Q_N = 20\text{ g} \times 4.75 = 95\text{ g}$
Ginger-Garlic paste: $Q_N = 15\text{ g} \times 4.75 = 71.25\text{ g}$
Butter: $Q_N = 30\text{ g} \times 4.75 = 142.5\text{ g}$
Fresh Cream: $Q_N = 60\text{ ml} \times 4.75 = 285\text{ ml}$
Red Chilli Powder: $Q_N = 5\text{ g} \times 4.75 = 23.75\text{ g}$
Turmeric Powder: $Q_N = 2.5\text{ g} \times 4.75 = 11.875\text{ g}$
Coriander Powder: $Q_N = 5\text{ g} \times 4.75 = 23.75\text{ g}$
Garam Masala: $Q_N = 5\text{ g} \times 4.75 = 23.75\text{ g}$
Salt: $Q_N = 5\text{ g} \times 4.75 = 23.75\text{ g}$
Oil: $Q_N = 30\text{ ml} \times 4.75 = 142.5\text{ ml}$
Water: $Q_N = 120\text{ ml} \times 4.75 = 570\text{ ml}$
Kasuri Methi: $Q_N = 2\text{ g} \times 4.75 = 9.5\text{ g}$

Answer

For 19 people ( $4$ family members $+ 15$ guests), using a scaling factor of $4.75$ , the required quantities are:

Paneer: $1187.5\text{ g}$
Tomatoes: $1425\text{ g}$
Onions: $950\text{ g}$
Cashews: $95\text{ g}$
Ginger-Garlic paste: $71.25\text{ g}$
Butter: $142.5\text{ g}$
Fresh Cream: $285\text{ ml}$
Red Chilli Powder: $23.75\text{ g}$
Turmeric Powder: $11.875\text{ g}$
Coriander Powder: $23.75\text{ g}$
Garam Masala: $23.75\text{ g}$
Salt: $23.75\text{ g}$
Oil: $142.5\text{ ml}$
Water: $570\text{ ml}$
Kasuri Methi: $9.5\text{ g}$

Common Mistakes

Scaling Only for Guests: Scaling by $\dfrac{15}{4} = 3.75$ instead of adding the family members to get $19$ total servings ( $4 + 15 = 19$ ).
Unit Confusion: Mixing up units like grams ( $\text{g}$ ) and millilitres ( $\text{ml}$ ) when multiplying by the scaling factor.

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