Question

If a : b = 3 : 1 and b : c = 5 : 1 then find the value of
 `(a^3/{15b^2c})^3` 

Answer 1

a : b = 3 : 1

`therefore a/b = 3/1 ⇒ a = 3b`  ...(1)

b : c = 5 : 1

`b/c = 5/1 ⇒ b = 5c`   ...(2)

From (1) and (2), we have

a = 3 × 5c = 15c

`(a^3/(15b^2c))^3`

= `[ (15c)^3 / {15 xx (5c)^2 xx c}]^3`

= `([ 15 xx 15 xx 15c^3]/[ 15 xx 25c^2 xx c ])^3`

`=((15xx15xx15)/(15xx5xx5))^3`

`=(3xx3)^3`

= `(9)^3`

= 729