To solve the problem of determining who has more sweets between Amit and Radha, let's break it down step by step.
1. Understanding the relationships:
- Radha has [tex]\(\frac{3}{2}\)[/tex] times the sweets that Amit has.
- Amit has [tex]\(\frac{2}{3}\)[/tex] part of what Radha has.
2. Assigning variables:
- Let [tex]\( A \)[/tex] represent the amount of sweets Amit has.
- Let [tex]\( R \)[/tex] represent the amount of sweets Radha has.
3. Defining the relationships mathematically:
- According to the first statement, Radha has [tex]\(\frac{3}{2}\)[/tex] times the sweets Amit has:
[tex]\[
R = \frac{3}{2} A
\][/tex]
- According to the second statement, Amit has [tex]\(\frac{2}{3}\)[/tex] part of what Radha has:
[tex]\[
A = \frac{2}{3} R
\][/tex]
4. Verifying consistency:
- Substitute [tex]\( R = \frac{3}{2} A \)[/tex] into [tex]\( A = \frac{2}{3} R \)[/tex]:
[tex]\[
A = \frac{2}{3} \left( \frac{3}{2} A \right)
\][/tex]
Simplifying the right-hand side:
[tex]\[
A = \frac{2}{3} \times \frac{3}{2} A
\][/tex]
[tex]\[
A = 1 A \quad \text{(which is consistent)}
\][/tex]
5. Comparing the quantities:
- To easily compare the amounts, let's assume a convenient value for [tex]\( A \)[/tex]. Let [tex]\( A = 1 \)[/tex] unit of sweets.
- Applying [tex]\( R = \frac{3}{2} A \)[/tex]:
[tex]\[
R = \frac{3}{2} \times 1 = 1.5 \quad \text{units of sweets}
\][/tex]
6. Interpreting the results:
- Amit has 1 unit of sweets.
- Radha has 1.5 units of sweets.
Conclusion:
Radha has more sweets than Amit because she has 1.5 units of sweets while Amit only has 1 unit. The given ratios and relationships confirm that Radha's share exceeds Amit's share. Thus:
Radha has more sweets.
