Question

If 2a = 3b = 5c, then what is
a.b : c?

Answer 1

2a=3b=5c
divide by 30
So a/15= b/10= c/6=k (suppose)
So a= 15k, b=10k, c= 6k
a:b:c = 15k:10k:6k
15:10:6

Answer 2

a : b : c =15 : 10 : 6

Step-by-step explanation:

We have,

2a = 3b = 5c

To find, a : b : c = ?

Let 2a = 3b = 5c = k

∴ 2a = k ⇒ a = $\dfrac{k}{2}$

3b = k ⇒ b = $\dfrac{k}{3}$ and

5c = k ⇒ c = $\dfrac{k}{5}$

∴ a : b : c =$\dfrac{k}{2}:\dfrac{k}{3}:\dfrac{k}{5}$

$=\dfrac{1}{2}:\dfrac{1}{3}:\dfrac{1}{5}$

The LCM of 2, 3 and 5 is 30.

Multiplying by numerator 30, we get

$=\dfrac{30}{2}:\dfrac{30}{3}:\dfrac{30}{5}$

$=15:10:6$

Hence, a : b : c =15 : 10 : 6.