Proportional Reasoning - 1 | IT

Question 10

Context: Manjunath usually mixes 15 mL of coffee decoction with 35 mL of milk to make filter coffee (ratio 15 : 35). For 'lighter' coffee, he mixes 10 mL of coffee and 40 mL of milk, making the ratio 10 : 40.

Q. Why is this coffee lighter?

Solution

To understand why the coffee is lighter, we compare the proportion of coffee decoction in each mixture.

Step 1 — Calculate coffee proportion for normal coffee

First, let us find the total volume of the normal coffee mixture. We add the volume of coffee decoction and milk.

$\text{Total volume (normal)} = \text{Coffee decoction} + \text{Milk}$

$= 15 \text{ mL} + 35 \text{ mL}$

$\boxed{50 \text{ mL}}$

Now, we find the proportion of coffee decoction in this mixture. The proportion is the amount of coffee divided by the total volume.

$\text{Proportion of coffee (normal)} = \frac{\text{Volume of coffee decoction}}{\text{Total volume}}$

$= \frac{15 \text{ mL}}{50 \text{ mL}}$

$= \frac{3}{10}$

$\boxed{0.3}$

This means that 30% of the normal coffee is decoction.

Step 2 — Calculate coffee proportion for lighter coffee

Next, let us find the total volume of the lighter coffee mixture. We add the volume of coffee decoction and milk.

$\text{Total volume (lighter)} = \text{Coffee decoction} + \text{Milk}$

$= 10 \text{ mL} + 40 \text{ mL}$

$\boxed{50 \text{ mL}}$

Now, we find the proportion of coffee decoction in this mixture. The proportion is the amount of coffee divided by the total volume.

$\text{Proportion of coffee (lighter)} = \frac{\text{Volume of coffee decoction}}{\text{Total volume}}$

$= \frac{10 \text{ mL}}{50 \text{ mL}}$

$= \frac{1}{5}$

$\boxed{0.2}$

This means that 20% of the lighter coffee is decoction.

Step 3 — Compare the proportions

We compare the proportion of coffee decoction in both mixtures. For normal coffee, the proportion is 0.3. For lighter coffee, the proportion is 0.2.

Since $0.2 < 0.3$ , the lighter coffee has less coffee decoction. A lower proportion of coffee decoction makes the coffee less strong.

Answer

The 'lighter' coffee has a lower proportion of coffee decoction (0.2 or 20%) compared to the normal coffee (0.3 or 30%). This lower concentration of coffee decoction makes the coffee less strong, or 'lighter'.

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Context: Manjunath usually mixes 15 mL of coffee decoction with 35 mL of milk to make filter coffee (ratio 15 : 35). For 'stronger' coffee, he mixes 20 mL of decoction with 30 mL of milk (ratio 20 : 30).

Q. Why is this coffee stronger?

Q10

Q. Why is this coffee lighter?

Q11

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.

Q12

Does the drawing look more realistic if the ratios are proportional? Why? Why not?

Q13

Puneeth’s father went from Lucknow to Kanpur in 2 hours by riding his motorcycle at a speed of 50 km/h. If he drives at 75 km/h, how long will it take him to reach Kanpur? Can we form this problem as a proportion—

Would it take Puneeth’s father more time or less time to reach Kanpur? Think about it.

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Context: The volume of a sachet is 6 mL and its price is ₹2. The volume of a small bottle is 180 mL and its price is ₹154. The ratio of the volume of a sachet to a small bottle is 6 : 180. The ratio of their prices is 2 : 154.

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Q16

Context: You have 12 countable objects or counters to share between the two of you.

Q. If your partner gets 5 counters, how many objects will you get? What is the ratio of the counters?