UPSC CDS I 2025 Mathematics Paper

The initial mixture contains kerosene and turpentine oil in the ratio $3:2$.Total mixture $=100\,\mathrm{L}$Kerosene $= \frac{3}{5} \times 100 = 60\,\mathrm{L}$Turpentine oil $= \frac{2}{5} \times 100 = 40\,\mathrm{L}$Final kerosene percentage $=20\%$Formula used:Final kerosene in the mixture $=$ Total mixture $\times ($ Final kerosene percentage $\div 100)$Additional kerosene to be added = Final kerosene - Initial keroseneCalculation:Let the additional kerosene to be added $= x\,\mathrm{L}$.Total mixture after adding kerosene $=100+ x\,\mathrm{L}$Kerosene in the new mixture $=60+x\,\mathrm{L}$For $20\%$ kerosene in the final mixture:$\; \Rightarrow \frac{60+x}{100+x} = \frac{20}{100}$$\; \Rightarrow (60+x) = \left(\frac{20}{100}\right) \times (100+x)$$\; \Rightarrow 60+x = \frac{20 \times (100+x)}{100}$$\; \Rightarrow 60+x = \frac{2000+20x}{100}$$\; \Rightarrow 100(60+x) = 2000+20x$$\; \Rightarrow 6000+100x = 2000+20x$$\; \Rightarrow 6000-2000 = 20x-100x$$\; \Rightarrow 4000 = -80x$$\; \Rightarrow x = \frac{-4000}{80}$$\; \Rightarrow x = -50$