Question

For each question, there are four options, out of which one is correct.
 $ 1. $ If $ 2A = 3B $ and $ 4B = 5C $ then $ A:C = ? $
A. $ 4:3 $
B. $ 8:15 $
C. $ 3:4 $
D. $ 15:8 $

Answer 1

Hint: Here we are given two equations: first find the correlation between two as per the desired ratio and then simplify by removing the common factors from the numerator and denominator for the required value.

Complete step-by-step answer:
Take the given expressions: $ 2A = 3B $
Make “A” the subject and move other terms on the opposite side. When you move a term multiplicative on one side to the opposite side then it goes to the denominator.
 $ A = \dfrac{{3B}}{2} $ …… (I)
Now, take the second given expression –
 $ 4B = 5C $
Make “C” the subject and move other terms on the opposite side. When you move a term multiplicative on one side to the opposite side then it goes to the denominator.
 $ C = \dfrac{{4B}}{5} $ …… (II)
From the equations (I) and (II)
 $ A:C = \dfrac{{\dfrac{{3B}}{2}}}{{\dfrac{{4B}}{5}}} $
Simplify the above expression, the numerator's denominator goes to the denominator and the denominator’s denominator goes to the numerator.
 $ A:C = \dfrac{{3B}}{2} \times \dfrac{5}{{4B}} $
Common factors from the numerator and the denominator cancel each other and therefore remove “B” from the numerator and the denominator of the above expression.
 $ A:C = \dfrac{3}{2} \times \dfrac{5}{4} $
Simplify the above expression finding the product of the terms –
 $ A:C = \dfrac{{15}}{8} $
The above expression can be re-written as –
 $ A:C = 15:8 $
From the given multiple choices – the option D is the correct answer.
So, the correct answer is “Option D”.

Note: Ratio is defined as the comparison between the two terms. When the ratio of the terms is taken, it is always taken on both sides. The term on the left hand side of one equation is placed upon the left hand side of the second equation and the same is applied for both sides of the equation.