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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

9 x

and

5 x

when multiplied by x.

9 x

is therefore the bigger number, while

5 x

is the smaller one.
Given that the larger number is increased by 9, or

9 x + 9

,
If 5 is taken out of the lower number, the result is

5 x - 5

.
The current values are

9 x + 9

and

5 x - 5 .

The smaller number is tripled by the larger one in the following equation:

9 x + 9 = 3 (5 x - 5)

= > 9 x + 9 = 15 x - 15

= > 6 x = 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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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: