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**Ans: Let Madhu took Rs. a and Vikash took Rs. b**

**Let the rate of interest was r% per annum**

**They lent Rs. (a + b) to Nikhil at the rate of (r + 2)% per annum**

**For Madhu,**

**The total interest received on Rs a = a \times 4 \times \frac{(r+2)}{100}**

**The total interest paid by Madhu to the bank = a\times r \times \frac{4}{100}**

**The total interest earned by Madhu after paying the interest to the bank**

**a \times 4 \times \frac{(r+2)}{100} - a\times r \times \frac{4}{100} = \frac{8a}{100} ------- (1)**

**For Vikash,**

**The total interest received on Rs. b = b \times 4 \times \frac{(r+2)}{100}**

**The total interest paid by Vikash to the bank = b\times r \times \frac{4}{100}**

**The total interest earned by Vikash after paying the interest to the bank**

**b \times 4 \times \frac{(r+2)}{100} - b\times r \times \frac{4}{100} = \frac{8b}{100} ------- (2)**

**From the question,**

**a – b = 50 × 100 = Rs. 5000**

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