# 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
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:
26 comments Page 1 of 3.

Ramzan said:   1 year ago
How we got 9x=99?
(7)

Vishal Bhagure said:   3 years ago
I am getting x = 8.

By taking 3 as common multiple and dividing the same by 12.

Sushant said:   4 years ago
@Bhavik you are wrong.

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)

Zainab said:   6 years ago
It can be slove like this please let me know?
New ration is;
12:23:=36.
36-9=33.
(5)

Vishal said:   6 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.
(2)

Juke said:   7 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.
(1)

Priya said:   7 years ago
@Ajit.

I also have the same doubt.

Can anyone explain us?

KOALA said:   8 years ago
Well said @Bharath.

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.
(9)