Question

The sum of three numbers is 212. If the ratio of he first to the second is 13:16 and that of he second to the third is 2:3, then find the numbers.
[Let the numbers be a a,b and c, then $\frac{a}{b}=\frac{13}{16}$ and $\frac{b}{c}=\frac{2}{3}=\frac{16}{24}$,
$i.e,a:b:c=13:16:24.$. Divide 212 in the ratio 13:16:24 to get the numbers.

Answer 1

Let the numbers be a,b,c.

$a+b+c=212$ _____ $1^{st}$ condition

$\frac{a}{b}=\frac{13}{16}$ $\frac{b}{c}=\frac{2}{3}$ ..... (given)

$\therefore a=\frac{13b}{16}$ $\therefore c=\frac{3b}{2}$

substituting in eq (1)

$\frac{13b}{16}+b+\frac{3b}{2}=212$

$b(\frac{13}{16}+1+\frac{3}{2})=212$

$b=64$

$\therefore a=\frac{13\times b}{16}=\frac{13\times 64}{16}=52$

$\therefore c=\frac{3b}{2}=\frac{3\times 64}{2}=96$.

$\therefore a=52$

$b=64$

$c=96$.