The following table shows the different ratios in which Manjunath mixes coffee decoction with milk. Write in the last column if the coffee is stronger or lighter than the regular coffee.

Question

Homi · Accepted Answer

We will determine the ratio of coffee decoction to milk for regular coffee and then compare this ratio with the ratios for other mixtures.

Step 1 — Determine the regular coffee ratio

The diagram shows three cups of coffee, all with the same proportions of coffee decoction and milk. This indicates that this proportion represents "regular" coffee. Let us examine the first row of the table to find this regular ratio. The coffee decoction is 300 mL and the milk is 600 mL. We calculate the ratio of coffee decoction to milk.

$\text{Ratio} = \frac{\text{Coffee Decoction}}{\text{Milk}}$

$= \frac{300 \text{ mL}}{600 \text{ mL}}$

$= \frac{1}{2}$

$= 0.5$

$\boxed{\text{Regular ratio} = 0.5}$

A coffee mixture is stronger if its ratio of coffee decoction to milk is greater than 0.5. A coffee mixture is lighter if its ratio of coffee decoction to milk is less than 0.5. A coffee mixture is regular if its ratio of coffee decoction to milk is equal to 0.5.

Diagram 1

Step 2 — Calculate and compare ratios for each row

We will calculate the ratio of coffee decoction to milk for each row and compare it to the regular ratio of 0.5.

Row 1: Coffee Decoction = 300 mL, Milk = 600 mL $\text{Ratio} = \frac{300}{600}$

$= 0.5$

Since $0.5 = 0.5$ , this coffee is Regular.

Row 2: Coffee Decoction = 150 mL, Milk = 500 mL $\text{Ratio} = \frac{150}{500}$

$= \frac{3}{10}$

$= 0.3$

Since $0.3 < 0.5$ , this coffee is Lighter.

Row 3: Coffee Decoction = 200 mL, Milk = 400 mL $\text{Ratio} = \frac{200}{400}$

$= \frac{1}{2}$

$= 0.5$

Since $0.5 = 0.5$ , this coffee is Regular.

Row 4: Coffee Decoction = 24 mL, Milk = 56 mL $\text{Ratio} = \frac{24}{56}$

We divide both numbers by their greatest common divisor, which is 8. $= \frac{24 \div 8}{56 \div 8}$

$= \frac{3}{7}$

To compare, we convert $\frac{3}{7}$ to a decimal: $\frac{3}{7} \approx 0.428$ . Since $0.428 < 0.5$ , this coffee is Lighter.

Row 5: Coffee Decoction = 100 mL, Milk = 300 mL $\text{Ratio} = \frac{100}{300}$

$= \frac{1}{3}$

To compare, we convert $\frac{1}{3}$ to a decimal: $\frac{1}{3} \approx 0.333$ . Since $0.333 < 0.5$ , this coffee is Lighter.

Answer

(i) Regular (ii) Lighter (iii) Regular (iv) Lighter (v) Lighter

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