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In 2010, the number of students appeared from state A increased by 10% and those from state B increased by 15% compared to the number of students from the respective states in 2009. Given that in 2009, the number of students from state A was 440 and from state B was 760, what is the ratio of the number of students from state A to state B in 2010?

Question

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In 2010, the number of students appeared from state A increased by 10% and those from state B increased by 15% compared to the number of students from the respective states in 2009. Given that in 2009, the number of students from state A was 440 and from state B was 760, what is the ratio of the number of students from state A to state B in 2010?

Accepted Answer

**Solution:**

1. Number of students from state A in 2009 = 440
2. Number of students from state B in 2009 = 760

3. Increase in students from state A in 2010 = 10% of 440 = $ \frac{10}{100} \times 440 = 44 $
   - So, students from state A in 2010 = 440 + 44 = 484

4. Increase in students from state B in 2010 = 15% of 760 = $ \frac{15}{100} \times 760 = 114 $
   - So, students from state B in 2010 = 760 + 114 = 874

5. Required ratio of students from state A to state B in 2010:
   $$
   \frac{484}{874} = \frac{242}{437} \quad \text{(after dividing numerator and denominator by 2)}
   $$

**Answer:** $242 : 437$

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