Question : If $ (a-b):(b-c):(c-d) =1:2:3$, then what is the value of $(a + d):c$ ?
Option 1: $1:2$
Option 2: $2:1$
Option 3: $4:1$
Option 4: $3:1$
Answer (1)
25th Jan, 2024
Correct Answer: $2:1$
Solution :
$\frac{a-b}{b-c}=\frac{1}{2}⇒2a+c = 3b$ ........(1)
$\frac{a-b}{c-d}=\frac{1}{3} ⇒3a-3b = c-d$ ........(2)
Substituting the value of $b$ from (1) in (2),
$3a-2a-c=c-d$
⇒ $a+d = 2c$
$\therefore (a + d):c = \frac{2c}{c} = 2:1$
Hence, the correct answer is $2:1$.
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