Proportional Reasoning - 1 | IT

Question 16

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?

Solution

Understand the Question

Total number of counters $= 12$ .
Your partner gets $5$ counters.
To find your share, subtract your partner's counters from the total ( $12 - 5 = 7$ ).
The ratio compares the two shares: $\text{Your counters} : \text{Partner's counters} = 7 : 5$ .

Step 1 · Calculate Your Counters

Given total counters $C_{\text{total}} = 12$ and partner's share $C_{\text{partner}} = 5$ . Diagram 1

\begin{aligned} C_{\text{you}} &= C_{\text{total}} - C_{\text{partner}} \\[0.6em] &= 12 - 5 \\[0.6em] &= 7 \end{aligned}

Step 2 · Determine the Ratio of the Counters

Comparing your counters to your partner's counters

\begin{aligned} R &= \text{Your counters} : \text{Partner's counters} \\[0.6em] &= 7 : 5 \end{aligned}

Answer

You will get $7$ counters, and the ratio of the counters is $7 : 5$ .

Common Mistakes

Reversing Ratio Order: Writing $5 : 7$ instead of $7 : 5$ . Always ensure the ratio matches the specified order (your share to partner's share).
Part-to-Whole Confusion: Stating $7 : 12$ or $5 : 12$ instead of comparing the two individual parts ( $7 : 5$ ).

More questions in IT

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In my school, there are 5 teachers and 170 students. The ratio of teachers to students in my school is $5 : 170$ . Count the number of teachers and students in your school. What is the ratio of teachers to students in your school? Write it below.

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

Q. Why is this coffee stronger?

Q10

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

Q. If you divide them equally, what is the ratio of the number of counters with each of you?

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?