Question : If a : b = c : d, then which of the following ratios is equal to a : c?
Option 1: a : d
Option 2: b : c
Option 3: a + d : b + c
Option 4: a + b : c + d
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Correct Answer: a + b : c + d
Solution : $a : b = c : d$ ⇒ $\frac{a}{b}$ = $\frac{c}{d}$ ⇒ $\frac{a}{b}$ + 1 = $\frac{c}{d}$ + 1 ⇒ $\frac{a+b}{b}$ = $\frac{c+d}{d}$ ⇒ $\frac{b}{d}$ = $\frac{a+b}{c+d}$ So, b : d = (a + b) : (c + d) Again, a : b =c : d ⇒ $\frac{a}{b}$ = $\frac{c}{d}$ ⇒ $\frac{a}{c}$ = $\frac{b}{d}$ Therefore, a : c = b : d = (a + b) : (c + d) Hence, the correct answer is (a + b) : (c + d).
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