The average salary of Santosh and Renu is Rs 3600. If Santosh's salary is increased by 50% and Renu's salary is increased by 30%, their combined total salary increases by 35%. What is the percentage by which Renu's salary is more or less than Santosh's salary before the increment?

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Accepted Answer

**Solution:**

1. Let Santosh's salary be $ S $ and Renu's salary be $ R $.

2. Given the average salary of Santosh and Renu is Rs 3600, so:
   $$
  $ \frac{S + R}{2} = 3600 \implies S + R = 7200$
   $$

3. After increment, Santosh's salary becomes $ S \times 1.5 $ and Renu's salary becomes $ $R \times 1.3$ $.

4. The total salary after increment is increased by 35%, so:
   $$
   $1.5S + 1.3R = 7200 \times 1.35 = 9720$
   $$

5. From the first equation, $ R = 7200 - S $.

6. Substitute $ R $ in the second equation:
   $$
   1.5S + 1.3(7200 - S) = 9720
   $$
   $$
   1.5S + 9360 - 1.3S = 9720
   $$
   $$
   (1.5 - 1.3)S = 9720 - 9360
   $$
   $$
   0.2S = 360
   $$
   $$
  $ S = \frac{360}{0.2} = 1800$
   $$

7. Using $ R = 7200 - S $, we get:
   $$
   R = 7200 - 1800 = 5400
   $$

8. Now, find the percentage by which Renu's salary is more than Santosh's salary before increment:
   $$
  $ \text{Percentage increase} = \frac{R - S}{S} \times 100 = \frac{5400 - 1800}{1800} \times 100 = \frac{3600}{1800} \times 100 = 200\% $
   $$

**Answer:** 200\%

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