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.

Hello friends,

Already this sum answer is given,
Let the original salaries of Ravi and Sumit be Rs. 2x and Rs. 3x respectively.
Then, 2x + 4000 = 40.
3x + 4000 = 57,
Till here you public know from where this come,
After that 6x = 68000, this is little bit question to us. From where this we got.

Here is the answer.

Across multiple,
57 (2x + 4000) =40 (3x + 4000).
2 * 3x = 6x, 57 - 40 = 17, 4000 is common.
6x = 17 * 4000.
6x = 68000. Here we solve sum doubt.

Going forward, we have to find Sumit salary.
6x = 68000 divide two as per the given ratio.
3x = 34000.

So here we got the value of 3x = 34000.

Sumit salary is 3x + 4000.
Therefore, 3x = 34000 + 4000.
Answer is 38000 Rs.

Let the salaries of Ravi and Sumit be and, respectively.
After increasing each salary by Rs. 4000, the new salaries become:

Ravi's new salary:
Sumit's new salary:


The ratio of their new salaries is given as . Therefore, we can write the equation:
frac{2x + 4000}{3x + 4000} = frac{40}{57}

Cross-multiply to eliminate the fraction:
57(2x + 4000) = 40(3x + 4000)

Expand both sides:
114x + 228000 = 120x + 160000

Simplify the equation:
228000 - 160000 = 120x - 114x
68000 = 6x

Solve for :
x = frac{68000}{6} = 11333.33
Sumit's original salary is :
3x = 3 times 11333.33 = 34000

Sumit's new salary:
3x + 4000 = 34000 + 4000 = 38000
Thus, Sumit's salary is Rs. 38,000.

What if we consider the two variable equations for this question.

Let the salary of Ravi of be Rs x and Sumit br Rs y.

Now, acc to question... two salary's are in the ratio 2:3.

Therefore, x/y=2/3.

=> 3x = 2y...........(1).

Acc to question if we add Rs 4000 to each salary.

Therefore, x+4000/y+4000 = 40/57.

=> 57x + 22800 = 40y + 16000.

=> 57x-40y = 160000-228000.........(2).

Acc to eq1..we multiply it by 19, it becomes,

57x = 38y.......(3).

Putting the value of (3) in (2)

=> 38y-40y = -68000.

=> -2y = -68000.

=> y = 34000.

So the salary of Sumit is Rs 34000

Let's denote Ravi's initial salary as 2x and Sumit's as 3x.

After the increase, their salaries become:
* Ravi: 2x + 4000
* Sumit: 3x + 4000

The new ratio is 40:57, so we can set up the following equation:
(2x + 4000)/(3x + 4000) = 40/57.

Cross-multiplying:
57(2x + 4000) = 40(3x + 4000)
Expanding:
114x + 228000 = 120x + 160000.

Simplifying:
6x = 68000.

Solving for x:
x = 11333.33.

Now, Sumit's initial salary was 3x. So, his initial salary is:
3 * 11333.33 = 34000
After the increase of Rs. 4000, Sumit's salary becomes:
34000 + 4000 = 38000
Therefore, Sumit's salary is Rs. 38,000.

Hai guys listen here...

the 2:3 ratio of Ravi & Sumith salary
2x:3x =>2x/3x
then
Salary increased by each 4000
2x+4000 ---------(1)
3x+4000----------(2)
let we write 2x+4000/3x+4000 (its become new ratio)
2x+4000/3x/4000=40/57 ratio
now solve this
57(2x+4000)=40(3x+4000)
114x+228000=120x+160000
114x-120x=228000-160000
6x=68000
now divided by 2
=> 3x=34000.

now we have 3x value is 34000
let subsitute equation no(2)
=>3x+4000
=>34000+4000
Ans =38000

ok bye...

@Shalini I agree.

The question "What is Sumit's salary?" should be more clear.

-Is it Sumit's "present" salary?

-Or is it Sumit's "new" salary?

At first, I thought the question was asking for Sumit's "current" salary. The answer should be Rs. 34, 000.

But the given answer is Rs. 38, 000. That is Sumit's "new" salary (34, 000+4, 000) ("If" he got the raise) not Sumit's "present" salary as written in the explanation.

Let original salary ravi and sumit be 2x and 3x.

If salary is increased by 4000.

So we can write 2x+4000 --- 1.

3x+4000 --- 2.

2x+4000/3x+4000 = 40/57.

Then 57(2x+4000) = 40(3x+4000).

57*2x+57*4000 = 40*3x + 40*4000.

114x - 120x = 228000 - 160000.

6x = 68000.
3x = 34000.

Sumits salary = 34000 + 4000 = 38000.

2x + 4000 = 40 ---> (1)
3x + 4000 = 57 ---> (2)

Now, multiply 2x + 4000 by 3 and 3x + 4000 by 2.

6x + 12000 = 120 ---> (3)
6x + 8000 = 114 ---> (4)

Now, subtract (4) from (3)
We get, 4000 = 6.

Now, we are asked to find Sumit's new salary.
We know, the ratio of new salaries of Ravi and Sumit is 40:57
Therefore, 4000 * 57/ 6 = 38000.

Sumit's new salary is RS. 38000.

Let the ratio of ravi & sumith salary Rs.2x And Rs.3x.

So it's tends for 2x/3x.

Salary increased by each 4000.

2x+4000 ------(1).
3x+4000 ------(2).

Let we write,
2x+4000/3x+4000= 40/57(this is new ratio given in Q).

57(2x + 4000) = 40(3x + 4000).
6x = 68,000.
3x = 34,000.

So, Sumit current Salary =3x+ 4000.
=34,000+4000.
=38,000.