Subjects algebra

Annual Income Bf7466

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1. **Stating the problem:** We need to find the annual income of Janathika Maratha given the tax slabs and the total tax paid of 15000 rupees. 2. **Understanding the tax slabs:** - First 500000 rupees: tax free (0%) - Next 500000 rupees: taxed at 4% - Next 500000 rupees: taxed at 8% 3. **Formula for tax calculation:** Total tax = Tax on first slab + Tax on second slab + Tax on third slab 4. **Calculate tax for each slab:** - Tax on first 500000 = $500000 \times 0 = 0$ - Tax on second 500000 = $500000 \times 0.04 = 20000$ - Tax on third 500000 = $500000 \times 0.08 = 40000$ 5. **Check total tax if income is 1500000:** Total tax = $0 + 20000 + 40000 = 60000$ 6. **Given total tax is 15000, which is less than 60000, so income is less than 1500000.** 7. **Let the income be $x$. Since tax on first 500000 is zero, tax applies only on amount above 500000.** 8. **If $x$ is between 500000 and 1000000, tax is 4% on $(x - 500000)$.** 9. **Set up equation:** $$15000 = 0.04 \times (x - 500000)$$ 10. **Solve for $x$:** $$x - 500000 = \frac{15000}{0.04} = 375000$$ $$x = 500000 + 375000 = 875000$$ **Final answer:** Janathika Maratha's annual income is **875000** rupees.