Question 62

Two numbers are in the ratio 2 : 3. If 5 is subtracted from the first number and six is added to the second number, then the ratio becomes 5 : 12. What would the ratio become when eight is added to each number?

Solution

Two numbers are in the ratio 2 : 3.

Let the two numbers are 2p and 3p respectively.

According to the problem,

$$\frac{2p-5}{3p+6}=\frac{5}{12}$$

24p - 60 = 15p + 30

9p = 90

p = 10

Required ratio = $$\frac{2p+8}{3p+8}=\frac{2\left(10\right)+8}{3\left(10\right)+8}=\frac{28}{38}=\frac{14}{19}$$

Hence, the correct answer is Option B

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