Question

The sum of three numbers is 123. The ratio of first to second number is 2:3.and the ratio of the second to the third is 4: 7. Find the third number.

• A. 42
• B. 24
• C. 63
• D. 81

Answer 1

The correct option is C

63

Sum of the three numbers is 123.
Ratio is $\frac{A}{B}=\frac{2}{3}$
Ratio of $\frac{B}{C}=\frac{4}{7}$
Now, we are trying to make the denominator of $\frac{a}{b}$ is same as numerator of $\frac{b}{c}$
$\frac{A}{B}=\frac{2\times 4}{3\times 4}=\frac{8}{12}$
$\frac{B}{C}=\frac{4\times 3}{7\times 3}=\frac{12}{21}$
So, the ration is 8: 12: 21
Let the constant = x
8x+12x+21x=123
Or, 41x=123
Or, x=3
So, third number C=21 $\times$ 3 = 63