The ratio of two number a and b is 3:5. If 2 is added to both the numbers, the ratio becomes 2:3. Find b?
- 10
- 5
- 15
- 8
Explanation
Given: a/b = 3/5 ... (1)
When 2 is added to both numbers, the ratio becomes 2/3, so we can write:
(a+2)/(b+2) = 2/3 ... (2)
Cross-multiplying (2), we get:
3(a+2) = 2(b+2)
Expanding and simplifying, we get:
3a + 6 = 2b + 4
Subtracting 6 from both sides gives:
3a = 2b - 2
Now, substituting (1) in the above equation, we get:
3(3/5)b = 2b - 2
Multiplying both sides by 5, we get:
9b = 10b - 10
Subtracting 10b from both sides gives:
-b = -10
Dividing both sides by -1, we get:
b = 10
So, the correct answer is: 10
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