1. **State the problem:** We have a studio apartment costing 64000, divided into labour, materials, and contractor's charges in ratio 12:15:5. 2. **Express individual costs:** Let the common ratio factor be $x$. Labour cost = $12x$ Materials cost = $15x$ Contractor's charges = $5x$ Total cost = $12x + 15x + 5x = 32x = 64000$ 3. **Find $x$:** $$x = \frac{64000}{32} = 2000$$ So, Labour cost = $12 \times 2000 = 24000$ Materials cost = $15 \times 2000 = 30000$ Contractor's charges = $5 \times 2000 = 10000$ 4. **After price increase:** Labour increases by $r$ percent. Materials increase by $2r$ percent. Contractor's charges remain the same. New labour cost = $24000 \times \left(1 + \frac{r}{100}\right)$ New materials cost = $30000 \times \left(1 + \frac{2r}{100}\right)$ 5. **Condition given:** New labour cost is two thirds the new materials cost. $$24000 \left(1 + \frac{r}{100}\right) = \frac{2}{3} \times 30000 \left(1 + \frac{2r}{100}\right)$$ 6. **Solve for $r$: ** $$24000 \left(1 + \frac{r}{100}\right) = 20000 \left(1 + \frac{2r}{100}\right)$$ Distribute: $$24000 + 24000 \times \frac{r}{100} = 20000 + 20000 \times \frac{2r}{100}$$ Simplify: $$24000 + 240r = 20000 + 400r$$ Bring variables to one side: $$24000 - 20000 = 400r - 240r$$ $$4000 = 160r$$ $$r = \frac{4000}{160} = 25$$ 7. **Calculate new costs:** New labour cost: $$24000 \times \left(1 + \frac{25}{100}\right) = 24000 \times 1.25 = 30000$$ New materials cost: $$30000 \times \left(1 + \frac{50}{100}\right) = 30000 \times 1.5 = 45000$$ Contractor's charges stay the same at 10000. 8. **Find new total cost:** $$30000 + 45000 + 10000 = 85000$$ **Final answers:** - $r = 25$ percent - New cost of building the apartment = 85000