Question

If 2a = 3b = 4c, then a: b: c =?
a) 2: 3: 4
b) 3: 4: 6
c) 4: 3: 2
d) 6: 4: 3

Answer 1

Hint:In the given question, we have been asked to find the value of a: b: c and it is given that 2a= 3b= 4c. In order to find the solution of this question, we first need to find the LCM of 2, 3, 4 and then dividing each individual term by the LCM of 2, 3, 4 i.e. 12. We will get the required solution.

Complete step by step solution:
We have been given that
2a = 3b = 4c
Taking the LCM 2, 3, 4
LCM OF 2, 3, 4 is 12.
Dividing each individual term by the LCM of 2, 3, 4 i.e. 12, we get
\[\Rightarrow \dfrac{2a}{12}=\dfrac{3b}{12}=\dfrac{4c}{12}\]
On simplifying, we get
\[\Rightarrow \dfrac{a}{6}=\dfrac{b}{4}=\dfrac{c}{3}\]
So,
Therefore, a: b: c = 6: 4: 3
Hence, option (d) is the correct answer.

Note: While solving these types of questions, students should always remember that to calculate the original values from a given ration we just require at least one constant in relation to each variable. The ratio is used to compare two given values. The important thing to recollect about any equation is that the ‘equals’ sign represents a balance. What the sign says is that what’s on the left-hand side is strictly an equal to what’s on the right-hand side. . It is the type of question where only mathematical operations such as addition, subtraction, multiplication and division is used.