Proportional Reasoning - 1 | IT

Question 9

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?

Solution

We compare the amount of coffee decoction in each cup to understand why one is stronger.

Step 1 — Proportion of decoction in normal coffee

Manjunath's first recipe is for normal coffee. Let us find the total volume of this coffee mixture. Total volume is the sum of decoction and milk.

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

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

Now, let us find the proportion of decoction in this coffee. The proportion of decoction is the ratio of decoction volume to total volume.

$= \frac{\text{Volume of decoction}}{\text{Total volume}}$

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

$= \frac{3}{10}$

$\boxed{0.3}$

This means that 0.3, or 30%, of the normal coffee is decoction.

Step 2 — Proportion of decoction in stronger coffee

Manjunath's second recipe is for stronger coffee. Let us find the total volume of this coffee mixture. Total volume is the sum of decoction and milk.

$= 20 \text{ mL} + 30 \text{ mL}$

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

Now, let us find the proportion of decoction in this coffee. The proportion of decoction is the ratio of decoction volume to total volume.

$= \frac{\text{Volume of decoction}}{\text{Total volume}}$

$= \frac{20 \text{ mL}}{50 \text{ mL}}$

$= \frac{2}{5}$

$\boxed{0.4}$

This means that 0.4, or 40%, of the stronger coffee is decoction.

Step 3 — Comparing the proportions

We compare the proportion of decoction in both coffee mixtures. For normal coffee, the proportion of decoction is 0.3. For stronger coffee, the proportion of decoction is 0.4. Since $0.4 > 0.3$ , the stronger coffee has a greater proportion of decoction. A higher proportion of decoction makes the coffee stronger.

Answer

The second coffee is stronger because it has a higher proportion of coffee decoction (0.4) in the total mixture compared to the first coffee (0.3).

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Q. Why is this coffee stronger?

Q10

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?

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.

Q14

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.

Q. Why do you think that the ratio of the prices is not proportional to the ratio of the volumes?

Q15

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

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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?