Question

Let ${ \frac{C}{5} = \frac{F - 32}{9}}$. If C lies between 10 and 20, then :

• A. 50 < F < 78
• B. 50 < F < 68
• C. 49 < F < 68
• D. 49 < F < 78

Answer 1

Answer: (B)

50 < F < 68

Answer 2

Given : ${ \frac{C}{5} = \frac{F - 32}{9}}$ and ${ 1 0< C < 20}$ ${\Rightarrow \:\: C = \frac{5 F - (32) 5}{9} }$ Since, ${10 < C < 20}$ $\Rightarrow \:\: { 10 < \frac{5 \, F - 160}{9} < 20}$ $\Rightarrow \:\: { 90 < 5 \, F - 160 < 180}$ $\Rightarrow \:\: {90 + 160 < 5 \, F < 180 + 160 }$ $\Rightarrow \:\: {250 < 5 F < 340 }$ $\Rightarrow \:\: { \frac{250}{5} < F < \frac{340}{5}}$ $\Rightarrow \:\: { 50 < F < 68 }$