A man spends 20\% of his income on rent and then uses 25\% of the remaining amount to buy clothes. The rest of his income is invested in Fixed Deposit (FD) and Recurring Deposit (RD) in the ratio 1:4. If the difference between the amount invested in FD and the amount spent on clothes is Rs 1680, what is the man's total income (in Rs)?

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Accepted Answer

**Solution:**

1. Let the man's total income be $ x $.

2. He spends 20\% of his income on rent, so the amount spent on rent is:
   $$
   0.20x
   $$

3. Remaining income after rent:
   $$
   x - 0.20x = 0.80x
   $$

4. He spends 25\% of the remaining income on clothes, so amount spent on clothes is:
   $$
   (0.25 )0.80x = 0.20x
   $$

5. Remaining income after clothes:
   $$
   0.80x - 0.20x = 0.60x
   $$

6. This remaining amount $ 0.60x $ is invested in FD and RD in the ratio 1:4.
   - Total parts = 1 + 4 = 5
   - Amount invested in FD:
     $$
    $$ \frac{1}{5} \times 0.60x = 0.12x$$
     $$
   - Amount invested in RD:
     $$
    $$ \frac{4}{5} \times 0.60x = 0.48x$$
     $$

7. According to the problem, the difference between the amount invested in FD and the amount spent on clothes is Rs 1680:
   $$
   0.20x - 0.12x = 1680
   $$

8. Simplify the equation:
   $$
   0.08x = 1680
   $$

9. Solve for $ x $:
   $$
   x = $$\frac{1680}{0.08} = 21000$$
   $$

**Answer:** Rs 21000

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