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Q.

The ratio of two numbers is 9:5. If 9 is added to the greater number and 5 is subtracted from the smaller number, the greater number becomes thrice the smaller one. Find the numbers:


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a

5 and 2

b

10 and 40

c

36 and 20

d

49 and 30 

answer is C.

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Detailed Solution

Concept: We multiply the ratio by a factor x to find the answer to this problem. Then, we adjust these figures as necessary to match the information provided in the inquiry. The answer is then obtained by solving for x.
From the above information, the ratio of the numbers is 9:5.
The ratios become 9x and 5x when multiplied by x.
9x is therefore the bigger number, while 5x is the smaller one.
Given that the larger number is increased by 9, or 9x + 9,
If 5 is taken out of the lower number, the result is 5x - 5.
The current values are 9x+9 and 5x -5. The smaller number is tripled by the larger one in the following equation:
9x + 9 = 3(5x - 5)
=> 9x + 9 = 15x -15
=> 6x = 24
=> x = 24/6
=> x = 4 
As a result, the numbers are 36 and 20, or 9x and 5x.
Hence, the correct option is 3.
 
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