Proportional Reasoning - 1 | IT

Question 15

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?

Solution

Understand the Question

We have a total of $12$ counters to be divided equally between $2$ people.
To find the ratio, we first determine the number of counters each person receives, and then express the relationship between their shares in simplest form as $\text{Share 1} : \text{Share 2}$ .

Step 1 · Divide the Counters

Diagram 1

\begin{aligned} \text{Number of counters per person} &= \text{Total counters} \div \text{Number of people} \\[0.6em] &= 12 \div 2 \\[0.6em] &= 6 \end{aligned}

Step 2 · Find the Ratio

The ratio of the number of counters with each person is:

\begin{aligned} \text{Ratio} &= (\text{Counters with Person 1}) : (\text{Counters with Person 2}) \\[0.6em] &= 6 : 6 \\[0.6em] &= 1 : 1 \end{aligned}

Answer

$1 : 1$

Common Mistakes

Not Simplifying the Ratio: Leaving the ratio as $6 : 6$ instead of dividing both terms by their greatest common divisor ( $6$ ) to simplify it to $1 : 1$ .
Stating the Count Instead of the Ratio: Giving the individual count of counters ( $6$ ) as the final answer rather than the ratio of the shares ( $1 : 1$ ).

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?