Aptitude - Ratio and Proportion - Discussion

Here is the best possible way I realised how they went from 6x to 3x.

If we follow the general standard:
Let the ratios be 2x and 3x.
Now we know that both get Rs. 4000, so it should look like this:

Ravi : (2x + 4,000)
Sami: (3x + 4,000)

Now they gave us the new ratio of what it would be after they got their added amount: 40 : 57.

By looking like this: (2x + 4,000) = 40 / (3x + 4,000) = 57 (Sorry for poor demonstration here)

By cross multiplying the values, it should look like this: 57(2x + 4,000) = 40(3x + 4,000)
We will then expand it out: 114x + 228,000 = 120x + 160,000
Then by simplifying it through this stage:
228,000 - 160,000 = 120x - 114x

The answer should look like this: 68,000 = 6x
It can also be written as: 6x = 68,000, it's still the same thing, just that 6x is on the other side for personal preference and ease of simplifying.

Now the problem is this instant go from 6x to 3x, but what is 6x? I don't know. My best possible answer is that it's nobodies amount and that you would rather want to find x, so that you could multiply is by 3 to get Sumit's salary:

Finding x (divide both sides by 6): 6x/6 = 68,000/6
x = 11333.333333333333333333333333333
Now multiply it by 3 -> 11333.333333333333333333333333333 * 3 = 34,000.

This is this only way I could rationally come to understand this jump from 6x to 3x and hopefully it has made sense to you.

Here are some questions I would like to respond to for some of the users:

@Tluanga Chhangte : The reason why you see it like that is because the actual way they should present the subtraction is like this:
(228,000 - 160,000 = 120x - 114x). The reason why x was on the left side on their sheet was possibly due to their minds having "x" on the left side and that is understandable as I do that myself sometimes.

The way this person did it: (114x-120x=228000-160000) would be quite miss guiding as if we refer to the expanded one from earlier:

(114x + 228,000 = 120x + 160,000), if you were to subtract, it would be: (114x - 120x = 160,000 - 228,000) which would still equal 6x = 68,000 as the two negatives would cancel eachother out when dividing to find "x". Hopefully, this has solved your confusion @Chhangte.

@Priyanka The solution to your problem should be pretty simple since we know what x is from my calculation. All that would need to be done is multiply x by 2 to get 2x:
(2 * 11333.333333333333333333333333333 = 22666.666666666666666666666666667 or Rs. 22,666.67 (2 d.p.)
Hopefully, this has solved your problem.


Hope it will helps to understand easily.

Why is 57 on the side of 2 and 40 on the side of 3 is 2 greater than 3 in a 2:3 ratio?

The shortcut formulae for these kinds of sums = (difference of new ratio/cross difference of both ratios )*increased value * require value.
= (57-40/120-114) * 4000 * 3.
= 17/6 * 12000.
=34000 =34000 + 4000(given in the question).

4000 should not be added because the question is if it increases, not increased. So, answer is 34000.

Thank you @Elumalai.

Then What is the Ravi salary?

Thank you @Elumalai.

But I have a question that, why did you divide 6x=68000 by 2?
where did 2 come from?

x= 680000÷6
3x+4000 we can write 3*680000÷6+4000=38000.

#Shortest solution#

Ravi's old salary =2p,
Sumit's old salary=3p,
Ravi's new salary =40q,
Sumit's new salary=57q.
40q -2p=4000 ---> 1
57q-3p=4000 ---> 2
On solving [1] &[2] we get q=2000/3,
So sumit's new salary is 57 * (2000/3)=3800.

@Vishal.

How you get the q value as 2000/3
Can you explain me?