Understanding the Commodity Price Problem

The question provides a set of relationships between the prices of six different commodities: P, Q, R, S, T, and U. We are given the price of one commodity, P, and asked to find the price of another, Q, by using the stated relationships.

Let's list the given relationships:

• The price of Q is 1.5 times that of T.
• The price of U is four times that of P.
• The price of S is equal to the price of R.
• The price of P is 3.5 times that of R.
• The price of T is twice the price of R.
• The price of P is Rs. 70.

We need to use these relationships to find the price of Q.

Step-by-Step Calculation of Commodity Prices

We will start with the known value, the price of P, and use the relationships to find the prices of other commodities until we can determine the price of Q.

Step 1: Find the price of R

We are given that the price of P is Rs. 70 and that the price of P is 3.5 times that of R. We can write this relationship as an equation:

\( \text{Price of P} = 3.5 \times \text{Price of R} \)

Substituting the known price of P:

\( 70 = 3.5 \times \text{Price of R} \)

To find the price of R, we divide the price of P by 3.5:

\( \text{Price of R} = \frac{70}{3.5} \)

Calculating the value:

\( \text{Price of R} = \frac{700}{35} = 20 \)

So, the price of R is Rs. 20.

Step 2: Find the price of T

We are given that the price of T is twice the price of R. We know the price of R from Step 1.

\( \text{Price of T} = 2 \times \text{Price of R} \)

Substituting the price of R:

\( \text{Price of T} = 2 \times 20 \)

\( \text{Price of T} = 40 \)

So, the price of T is Rs. 40.

Step 3: Find the price of Q

We are given that the price of Q is 1.5 times that of T. We know the price of T from Step 2.

\( \text{Price of Q} = 1.5 \times \text{Price of T} \)

Substituting the price of T:

\( \text{Price of Q} = 1.5 \times 40 \)

Calculating the value:

\( \text{Price of Q} = \frac{15}{10} \times 40 = \frac{3}{2} \times 40 \)

\( \text{Price of Q} = 3 \times 20 = 60 \)

So, the price of Q is Rs. 60.

Summary of Commodity Prices

Based on the given information and our calculations, we can determine the prices of some commodities:

We could also find the prices of S and U, although they were not required to answer the question about Q:

• Price of S = Price of R = Rs. 20
• Price of U = 4 \(\times\) Price of P = 4 \(\times\) 70 = Rs. 280

Final Answer

The price of commodity Q is Rs. 60.

Revision Table: Commodity Price Relationships

Additional Information: Solving Price Relationship Problems

Problems involving relationships between quantities, like commodity prices, can often be solved by setting up equations based on the given information. Here are some tips:

• Identify the known value(s).
• Identify the target value you need to find.
• Write down each relationship as a mathematical equation.
• Use substitution or step-by-step calculation starting from the known value to find the target value.
• Ensure units are consistent (in this case, all prices are in Rupees).
• Break down complex problems into smaller, manageable steps.

These types of problems test your ability to translate word statements into mathematical expressions and solve them systematically.