QQuestion
If x = \frac{5\mathrm{a}\mathrm{b}}{\mathrm{a}-\mathrm{b}}, a ≠ b,
(a) Find: \frac{\mathrm{x}}{\mathrm{a}}
(b) Using properties of proportion, find: \frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}-\mathrm{a}}
ICSEClass XMathematicsRatio And Proportion03 Mark2026 Easy
✓Answer
Given, x = \frac{5\mathrm{a}\mathrm{b}}{\mathrm{a}-\mathrm{b}}
(a) Dividing both sides by a:
\frac{\mathrm{x}}{\mathrm{a}}=\frac{1}{\mathrm{a}}\left(\frac{5\mathrm{a}\mathrm{b}}{\mathrm{a}-\mathrm{b}}\right)⇒ \frac{\mathrm{x}}{\mathrm{a}}=\frac{5\mathrm{b}}{\mathrm{a}-\mathrm{b}}
(b) Applying componendo and dividendo:
\frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}-\mathrm{a}}=\frac{5\mathrm{b}+(\mathrm{a}-\mathrm{b})}{5\mathrm{b}-(\mathrm{a}-\mathrm{b})}⇒ \frac{\mathrm{x}+\mathrm{a}}{\mathrm{x}-\mathrm{a}}=\frac{\mathrm{a}+4\mathrm{b}}{6\mathrm{b}-\mathrm{a}}
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