Question:
The ratio of two numbers is 4:5. But, if each number is increased by 20, the ratio becomes 6:7. The sum of such numbers is:
The ratio of two numbers is 4:5. But, if each number is increased by 20, the ratio becomes 6:7. The sum of such numbers is:
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When ratios change after equal increase, set variables using original ratio and use algebra to find unknowns.
Updated On: Aug 11, 2025
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The Correct Option is A
Solution and Explanation
Step 1: Let the numbers be 4x and 5x
Initial ratio = \(4x : 5x\) Step 2: Apply given condition
\[ \frac{4x + 20}{5x + 20} = \frac{6}{7} \] Step 3: Cross-multiply and solve
\[ 7(4x + 20) = 6(5x + 20) \Rightarrow 28x + 140 = 30x + 120 \Rightarrow 20 = 2x \Rightarrow x = 10 \] Step 4: Find the numbers and sum
\[ \text{First number} = 4x = 40
\text{Second number} = 5x = 50
\Rightarrow \text{Sum} = 40 + 50 = \boxed{90} \] % Final Answer \[ \boxed{90} \]
Initial ratio = \(4x : 5x\) Step 2: Apply given condition
\[ \frac{4x + 20}{5x + 20} = \frac{6}{7} \] Step 3: Cross-multiply and solve
\[ 7(4x + 20) = 6(5x + 20) \Rightarrow 28x + 140 = 30x + 120 \Rightarrow 20 = 2x \Rightarrow x = 10 \] Step 4: Find the numbers and sum
\[ \text{First number} = 4x = 40
\text{Second number} = 5x = 50
\Rightarrow \text{Sum} = 40 + 50 = \boxed{90} \] % Final Answer \[ \boxed{90} \]
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