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Let's break down the problem and solve it step by step.

### Given:
- The ratio of the prices of tea last year and this year is **5:6**.
- The ratio of the prices of coffee last year and this year is **7:8**.
- The sum of the prices of 1 kg of tea and 1 kg of coffee this year is **₹48**.
- The price of tea last year was **20/21** of the price of coffee last year.

### Let:
- The price of tea last year be \( T \).
- The price of tea this year be \( T' \).
- The price of coffee last year be \( C \).
- The price of coffee this year be \( C' \).

From the given ratios:
\[
\frac{T}{T'} = \frac{5}{6} \quad \text{or} \quad T' = \frac{6}{5}T
\]
\[
\frac{C}{C'} = \frac{7}{8} \quad \text{or} \quad C' = \frac{8}{7}C
\]

We are also given that the total price this year is ₹48, so:
\[
T' + C' = 48
\]

Substitute the expressions for \( T' \) and \( C' \):
\[
\frac{6}{5}T + \frac{8}{7}C = 48 \tag{1}
\]

Finally, the price of tea last year is related to the price of coffee last year by:
\[
T = \frac{20}{21}C \tag{2}
\]

### Step 1: Substitute equation (2) into equation (1)

Substitute \( T = \frac{20}{21}C \) into equation (1):
\[
\frac{6}{5} \times \frac{20}{21}C + \frac{8}{7}C = 48
\]
Simplify each term:
\[
\frac{6 \times 20}{5 \times 21}C + \frac{8}{7}C = 48
\]
\[
\frac{120}{105}C + \frac{8}{7}C = 48
\]
Simplify the fractions:
\[
\frac{24}{21}C + \frac{8}{7}C = 48
\]
Find a common denominator:
\[
\frac{24}{21}C + \frac{24}{21}C = 48
\]
Add the fractions:
\[
\frac{48}{21}C = 48
\]
Solve for \( C \):
\[
C = 48 \times \frac{21}{48} = 21
\]

So, the price of coffee last year, \( C \), is ₹21.

### Step 2: Find the price of tea last year

Now, using equation (2):
\[
T = \frac{20}{21} \times 21 = 20
\]

Thus, the price of tea last year was **₹20**.

Would you like any further details or have any questions?

Here are some related questions to think about:
1. How would the solution change if the price of coffee this year increased at a different rate?
2. Can we generalize this method for any pair of ratios between two years?
3. How would we adjust the calculation if the sum of prices this year was different?
4. What if the relationship between tea and coffee prices last year was different from 20/21?
5. Can you derive a formula to calculate the prices based on similar problems?

**Tip:** When solving problems involving ratios, always express unknowns in terms of a common variable, making substitution easier.

The ratio of the prices of tea last year and this year is 5:6. The ratio of the prices of coffee last year and this year is 7:8. The sum of the prices of a kg of tea and a kg of coffee this year is ₹48. Find the price of tea (in ₹) last year if it was 20/21 of the price of coffee last year.

Learn how to solve a ratio problem involving the prices of tea and coffee using algebra. This problem covers key concepts like ratios, linear equations, and proportions. Suitable for students in Grades 8-10.

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