Question

Which of the following is/are correct?

• A. $2:7::n:21$, n = 5
• B. $2:7::n:21$, n = 6
• C. $7:15::49:n$, n = 105
• D. $7:15::49:n$, n = 106

Answer 1

Answer: (B), (C)

$7:15::49:n$, n = 105

Four numbers in proportion a:b::c:d can be written as
$\frac{a}{b}=\frac{c}{d}$
By cross multiplication

$\Rightarrow a\times d=b\times c$

Option A: $2:7::n:21$
$\Rightarrow \frac{2}{7}=\frac{n}{21}$
On cross - multiplication,

$2\times 21=7\times n$
$n=6$
Option A is incorrect.

Option B: $2:7::n:21$, n = 6
$\Rightarrow \frac{2}{7}=\frac{n}{21}$
On cross - multiplication,

$2\times 21=7\times n$
$n=6$
Option B is correct.

Option C: $7:15::49:n$
$\Rightarrow \frac{7}{15}=\frac{49}{n}$
On cross - multiplication,

$7\times n=49\times 15$
$n=105$
Option C is correct.

Option D: $7:15::49:n$
$\Rightarrow \frac{7}{15}=\frac{49}{n}$
On cross - multiplication,

$7\times n=49\times 15$
$n=105$
Option D is incorrect.