Aptitude - Ratio and Proportion - Discussion

Discussion Forum : Ratio and Proportion - General Questions (Q.No. 14)
14.
Two number are in the ratio 3 : 5. If 9 is subtracted from each, the new numbers are in the ratio 12 : 23. The smaller number is:
27
33
49
55
Answer: Option
Explanation:

Let the numbers be 3x and 5x.

Then, 3x - 9 = 12
5x - 9 23

23(3x - 9) = 12(5x - 9)

9x = 99

x = 11.

The smaller number = (3 x 11) = 33.

Discussion:
27 comments Page 1 of 3.

Bharath said:   8 years ago
This question can be solved very easily.

Here the first ratio is a : b :: 3 : 5 that means "a" should be in multiples of 3 so the answer in the option must be either 33 or 27.

The next part is it is subtracted by 9 then the answer should satisfy ratio 12 : 23. So if 27 - 9 = 18 it is not multiple of 12 but 33 - 9 = 24.

24 is multiple of 12 so 24 is the answer.
(12)

Juke said:   8 years ago
Let x be the smaller number.
y be the larger number.

1st equation:
(x/y)=(3/5)

2nd equation:
(x-9)/(y-9)=12/23.

Then solve for x and y.
x = 33 and y = 55.

Though my solution is different i still arrive at the same answer.
I think my equation is easy to understand.
(2)

Ajit said:   8 years ago
The two number should be X &Y and then their proportion is 3:5 then the sum will be 3x - 9/5y - 9 = 12/23.

23 (3x - 9) = 12 (5y - 9) => 69x - 207 = 60y - 108 = > 69x - 69y = 207 - 108 then what to do? Please tell me.

Gerald said:   1 decade ago
@Chandan.

From the question they gave new ratio as 12:23 so from the answer 3 * 11 =33. 33-9 =24. and 5 * 11 =55, 55-9=46, then it is in the ration of 24:46, therefore divide both by 2 you will get the new ratio of 12:23.

Vishal said:   7 years ago
Easy and best way Subtract 1st number to 2nd number of new ratio i.e. 12-23.

So, the difference = 11 so we got each fraction number for ration so, 11 per fraction * small 1st ratio number i.e.3 so, 11*3=33.
(7)

ADITYA MISHRA said:   9 years ago
3/5=2R (5-3=2 i.e. difference).

12/23=11R (23-12=11).

3/5*11 multiply by 2nd difference = 33/55.

12/23*2 multiply by 1st difference = 24/46.

9R = 9 i.e R = 1. So that smaller no 33.

Rahul said:   9 years ago
Hi, I got this as answer, am I right?

(3x - 9)/(5x - 9) = 12/23.
3(x - 3)/(5x - 9) = 12/23.
(x - 3)/(5x - 9) = 4/23.
23 * (x - 3) = 4 * (5x - 9).
23x - 69 = 20x - 45.
3x = 24.
x = 8.

Francis Vivian said:   7 months ago
x/y = 3/5 -> y = 5x/3.

-> (x-9) / (y-9) = 12/23.
-> 23(x-9) = 12(y-9).
-> 23x - 207 = 12y - 108.
-> 23x - 12(5x/3) = 207 - 108.
-> 3x = 99.
-> x = 99/3 = 33.
(2)

Chandan said:   1 decade ago
In question they told each number is subtracted from 9. Then the answer would be (3*11) - 9 = 24. But they've not given 24 as the option to choose.

Bhavik said:   5 years ago
x/y = 3/5. Than,
x-9/y-9 = 12/23.

Now solve both the equation.
23x-12y=99 and 5x-3y=0.

Therefore x=33 and y=55.
So smaller no. is 33.
(3)


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