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If two number are in the ratio 2 : 3 and the ratio becomes 3 : 4 when 8 is added to both the numbers, then the sum of the two numbers is = ?
Answer & Solution
Correct Answer:
Option
D
Let the 2 number be (2x, 3x)
According to the question,
$$\eqalign{ & \Rightarrow \frac{{2x + 8}}{{3x + 8}} = \frac{3}{4} \cr & \Rightarrow 8x + 32 = 9x + 24 \cr & \Rightarrow x = 8 \cr} $$
Therefore, the sum of the two numbers is
= 2x + 3x = 5x
= 5 × 8 = 40
According to the question,
$$\eqalign{ & \Rightarrow \frac{{2x + 8}}{{3x + 8}} = \frac{3}{4} \cr & \Rightarrow 8x + 32 = 9x + 24 \cr & \Rightarrow x = 8 \cr} $$
Therefore, the sum of the two numbers is
= 2x + 3x = 5x
= 5 × 8 = 40
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