Question

Two numbers are in the ratio \(4:5\). Their LCM is 240. Find the sum of numbers.

• A. \(108\)
• B. \(180\)
• C. \(120\)
• D. \(105\)
• E. \(125\)

Answer 1

The Correct Option is A

Concept: If two numbers are in ratio \(a:b\), they can be written as: \[ ak \text{ and } bk \] LCM of numbers: \[ \text{LCM} = k \times \text{LCM}(a,b) \]
Step 1: Assume numbers.
\[ \text{Numbers} = 4k \text{ and } 5k \]
Step 2: Use LCM formula.
\[ \text{LCM} = k \times \text{LCM}(4,5) = k \times 20 \] \[ k \times 20 = 240 \Rightarrow k = 12 \]
Step 3: Find numbers.
\[ 4k = 48,\quad 5k = 60 \]
Step 4: Find sum.
\[ 48 + 60 = 108 \]
Step 5: Option analysis.

• (A) 108: Correct \checkmark
• (B) 180: Incorrect $\times$
• (C) 120: Incorrect $\times$
• (D) 105: Incorrect $\times$
• (E) 125: Incorrect $\times$

Conclusion:
Thus, the correct answer is
Option (A).