The World of Numbers | Exercise 3.1

Question 1

A merchant in the port city of Lothal is exchanging bags of spices for copper ingots. He receives 15 ingots for every 2 bags of spices. If he brings 12 bags of spices to the market, how many copper ingots will he leave with?

Solution

Understand the Question

The exchange rate is given as $15\text{ copper ingots}$ for every $2\text{ bags of spices}$ .
To find the total number of ingots obtained for $12\text{ bags of spices}$ , determine the number of ingots received per bag (or find how many 2-bag groups are in $12\text{ bags}$ ) and multiply accordingly.

Step 1 · Calculate Ingots per Bag

Given exchange rate: $2\text{ bags} = 15\text{ ingots}$ Diagram 1

\begin{aligned} 1\text{ bag} &= \dfrac{15}{2}\text{ ingots} \\[0.6em] &= 7.5\text{ ingots} \end{aligned}

Step 2 · Calculate Total Ingots for 12 Bags

For $12\text{ bags}$ of spices:

\begin{aligned} \text{Total ingots} &= 12 \times 7.5 \\[0.6em] &= 90 \end{aligned}

Answer

90 copper ingots

Common Mistakes

Inverting the Ratio: Dividing $2$ by $15$ instead of $\dfrac{15}{2}$ , which incorrectly calculates bags per ingot instead of ingots per bag.
Skipping the Group Size: Multiplying $12 \times 15 = 180$ directly without dividing by $2$ , forgetting that $15\text{ ingots}$ corresponds to $2\text{ bags}$ , not $1\text{ bag}$ .

Question 1

More questions in Exercise 3.1