Question

The L.C.M of two numbers is 48. The numbers are in the ratio 2:3. Then the sum of the number is:
A.40
B.50
C.60
D.35

Answer 1

Hint: (i) Here, we are going to use the definition of L.C.M
(ii) One should start by considering the total ratio first and then determine the numbers using their relation with the ratio given.

Complete step-by-step answer:
Given, the L.C.M of two numbers is 48. The numbers are in the ratio 2:3
We know that the L.C.M is the least common multiple or a number that can be fairly divided by the numbers taken initially.
Let us suppose the total ratio be equal to \[x\]
Since, the numbers are in the ratio 2: 3. Therefore the numbers are \[2x\] and \[3x\]
Then L.C.M (\[2x\],\[3x\])=\[6x\]
\[\begin{gathered}
   \Rightarrow 6x = 48 \\
   \Rightarrow x = 8 \\
\end{gathered} \]
So, the numbers are \[2x = 2 \times 8 = 16\] and \[3x = 3 \times 8 = 24\]
Which implies the sum of the two numbers is \[16 + 24 = 40\]
Therefore, option A.40 is the required solution

Note: (i) Since\[x\] was common among both the numbers therefore L.C.M comes out to be \[6x\] and not \[6{x^2}\]
(ii) The questions containing ratios should always be approached by finding the total ratio using an unknown variable.