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Two number are in the ratio of 2:3. If 9 (Nine) is added to each number, they will be in ratio 3:4. What is the product of the two numbers?

Solution

✅ Correct Option: 3

The numbers are in the ratio 2:32:3, so take them as 2x2x and 3x3x.

Adding 9 to each:

2x+93x+9=34\dfrac{2x+9}{3x+9}=\dfrac{3}{4}

Cross multiply:

4(2x+9)=3(3x+9)4(2x+9)=3(3x+9)

⇒8x+36=9x+27\Rightarrow 8x+36=9x+27

⇒x=9\Rightarrow x=9


The numbers are 2x=182x=18 and 3x=273x=27.

Product=18×27=486\text{Product}=18\times27=486

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