Question : The sum of three numbers is 126. If the ratio of the first to third is 3 : 7 and that of the second to third is 4 : 7, then what is the second number?
Option 1: 36
Option 2: 27
Option 3: 63
Option 4: 56
Correct Answer: 36
Solution :
Let the three numbers as $a, b,$ and $c,$ respectively.
Given that the sum of the three numbers is 126, we have:
$a + b + c = 126$ --------------------(1)
It's also given that the ratio of the first to third is 3 : 7 and that of the second to third is 4 : 7.
$\Rightarrow \frac{a}{c} = \frac{3}{7}$
$\Rightarrow a = \frac{3}{7}c$
Also, $\frac{b}{c} = \frac{4}{7}$
$\Rightarrow b = \frac{4}{7}c$
Substituting these values into the first equation, we get:
$\Rightarrow \frac{3}{7}c + \frac{4}{7}c + c = 126$
$\Rightarrow \frac{14}{7}c = 126$
$\Rightarrow c = 63$
Substituting c into the equation for b.
$\Rightarrow b = \frac{4}{7} \times 63 = 36$
Hence, the correct answer is 36.
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