Question

If $a:b=3:1$ nd $b:c=5:1$ then find the value of

• A. ${\left(\frac{a^3}{15b^{2}c}\right)}^3$
• B. $\frac{a^2}{7bc}$
• C. both a and b
• D. none of this

Answer 1

The correct option is B $\frac{a^2}{7bc}$

Given that,

$a:b=3:1$ and $b:c=5:1$

$⟹a:b=15:5$ and $b:c=5:1$

$\therefore a:b:c=15:5:1$

Let, $a=15k$ then $b=5k,c=k$

$\left(i\right){\left(\frac{a^3}{15b^{2}c}\right)}^3={\left(\frac{15k\times 15k\times 15k}{15\times 5k\times 5k\times k}\right)}^3=(3\times 3{)}^3=9^3=729$

$\left(ii\right)\frac{a^2}{7bc}=\frac{15k\times 15k}{7\times 5k\times k}=\frac{15\times 3}{7}=\frac{45}{7}$