Question 1

We use proportional reasoning to scale ingredient quantities based on the number of servings.

Step 1 — Ingredients for family

First, we list the ingredients and their quantities for our family. Our family has 4 members. Our favourite dish is Paneer Butter Masala. The ingredients and their quantities for 4 people are as follows:

Paneer: 250 g.

Tomatoes: 300 g.

Onions: 200 g.

Cashews: 20 g.

Ginger-Garlic paste: 15 g.

Butter: 30 g.

Fresh Cream: 60 ml.

Red Chilli Powder: 5 g.

Turmeric Powder: 2.5 g.

Coriander Powder: 5 g.

Garam Masala: 5 g.

Salt: 5 g.

Oil: 30 ml.

Water: 120 ml.

Kasuri Methi: 2 g.

Step 2 — Calculate total servings

Next, we find the total number of people for the festival. This includes our family members and the invited guests. Let $N_F$ be the number of family members. Let $N_G$ be the number of guests. Let $N_T$ be the total number of people.

$N_F = 4 \text{ people}$

$N_G = 15 \text{ people}$

$N_T = N_F + N_G$

$N_T = 4 + 15$

$\boxed{N_T = 19 \text{ people}}$

Step 3 — Determine the scaling factor

We need to find how many times larger the new quantity should be. This is called the scaling factor. Let $S$ be the scaling factor. The scaling factor is the ratio of total people to family members.

$S = \frac{\text{Total people}}{\text{Family members}}$

$S = \frac{N_T}{N_F}$

$S = \frac{19}{4}$

$S = 4.75$

$\boxed{S = 4.75}$

Step 4 — Calculate new ingredient quantities

Now, we multiply each original ingredient quantity by the scaling factor. Let $Q_O$ be the original quantity. Let $Q_N$ be the new quantity.

For Paneer, the new quantity is: $Q_N = 250 \text{ g} \times 4.75$

$\boxed{1187.5 \text{ g}}$

For Tomatoes, the new quantity is: $Q_N = 300 \text{ g} \times 4.75$

$\boxed{1425 \text{ g}}$

For Onions, the new quantity is: $Q_N = 200 \text{ g} \times 4.75$

$\boxed{950 \text{ g}}$

For Cashews, the new quantity is: $Q_N = 20 \text{ g} \times 4.75$

$\boxed{95 \text{ g}}$

For Ginger-Garlic paste, the new quantity is: $Q_N = 15 \text{ g} \times 4.75$

$\boxed{71.25 \text{ g}}$

For Butter, the new quantity is: $Q_N = 30 \text{ g} \times 4.75$

$\boxed{142.5 \text{ g}}$

For Fresh Cream, the new quantity is: $Q_N = 60 \text{ ml} \times 4.75$

$\boxed{285 \text{ ml}}$

For Red Chilli Powder, the new quantity is: $Q_N = 5 \text{ g} \times 4.75$

$\boxed{23.75 \text{ g}}$

For Turmeric Powder, the new quantity is: $Q_N = 2.5 \text{ g} \times 4.75$

$\boxed{11.875 \text{ g}}$

For Coriander Powder, the new quantity is: $Q_N = 5 \text{ g} \times 4.75$

$\boxed{23.75 \text{ g}}$

For Garam Masala, the new quantity is: $Q_N = 5 \text{ g} \times 4.75$

$\boxed{23.75 \text{ g}}$

For Salt, the new quantity is: $Q_N = 5 \text{ g} \times 4.75$

$\boxed{23.75 \text{ g}}$

For Oil, the new quantity is: $Q_N = 30 \text{ ml} \times 4.75$

$\boxed{142.5 \text{ ml}}$

For Water, the new quantity is: $Q_N = 120 \text{ ml} \times 4.75$

$\boxed{570 \text{ ml}}$

For Kasuri Methi, the new quantity is: $Q_N = 2 \text{ g} \times 4.75$

$\boxed{9.5 \text{ g}}$

Answer

(i) My favourite dish is Paneer Butter Masala. (ii) The ingredients and their quantities needed for my family (4 members) are: Paneer: 250 g, Tomatoes: 300 g, Onions: 200 g, Cashews: 20 g, Ginger-Garlic paste: 15 g, Butter: 30 g, Fresh Cream: 60 ml, Red Chilli Powder: 5 g, Turmeric Powder: 2.5 g, Coriander Powder: 5 g, Garam Masala: 5 g, Salt: 5 g, Oil: 30 ml, Water: 120 ml, Kasuri Methi: 2 g. (iii) The quantities of ingredients required to cook the same dish for 15 guests (total 19 people) are: Paneer: 1187.5 g, Tomatoes: 1425 g, Onions: 950 g, Cashews: 95 g, Ginger-Garlic paste: 71.25 g, Butter: 142.5 g, Fresh Cream: 285 ml, Red Chilli Powder: 23.75 g, Turmeric Powder: 11.875 g, Coriander Powder: 23.75 g, Garam Masala: 23.75 g, Salt: 23.75 g, Oil: 142.5 ml, Water: 570 ml, Kasuri Methi: 9.5 g.