Aptitude - Ratio and Proportion - Discussion

@Stark Vin.

We are taking X because ratio means dividing the total quantity into some parts and the number of parts we divide them into is represented in the form of the ratio.

For example, if I have 30 chocolates and if I want to divide them in the ratio 1:2 then first I will see into how many equal parts I need to divide the chocolates into that is 3 in this case why? Because ratio is 1:2 that is to parts I want is 3. That means I need to divide 30 into 3 equal parts and then take 1 part on one side and other part on the other side. This simply means if I divide 30 by 3 I get 10. This means I divided 30 into 3 equal parts where each part contains 10 chocolates. Now I need to divide them in the ratio 1:2 so I take 10 chocolate on one side which is one part of 30 in this example and remaining 2 parts which add up to 20 in other parts. Now 10 by 20 equals 1 by 2 or 1:2 that is what we call as ratio. That is ratio is the representation of total quantity in its simplest form. We could have written it as 10:20 by we need to simplify as much as possible so we take it as 1:2. Now coming to this question we have the boys to girls ratio as 7:8 that simply means the total strength was divide into 7+8 parts but since we do not know what is the total strength we take it as some variable say t now, t by 15 we assume as x. This means now I have divided total strength into 15 equal parts were each part contains x. In that 7x we take as number of boys and 8x as number of girls.

@Kiran Kumar

note that something we included to get 20%

For example the ratio of the ratio of to boys ages was 5:2
we can write it as 5x : 2x we get exact ratio we will not consider it alone

For that way 7x 8x will appear

then

to covert 20% into no. it will be 20/100

note that the unknown was x

then 20/100x*x

so we take common one x(20/100+1)

so x(20/100+100)

x(120/100)

that was we get 120/100
forget x because that x which is in 7x both are same so we get 120/100*7x

Given : B : G = 7:8.
This can be written as 7x : 8x ( X being the common multiplier).
Let x = 10 (For simple Calculation)
So Boys = 70 & Girls = 80.
Increased Of Boys by 20% = 70*20/100 = 14.
So After Increase boys would be = 70 + 14 = 84.
Similarly Girls = 80*10/100 = 8 & Girls After Increase would be = 80 + 8 = 88.

New Boys : New Girls = 84:88.
Simply 21:22.

Herre the ration is; 7:8.
We take it as 7x : 8x.
Assume x = 10.
Then 7*10 : 8 * 10.
70 : 80.

Increment boys = 20%
The 70s 20% is 14.
So we add 70+14 = 84.

Similarly, we calculate girl's increment for 10%.

80s 10% is 8.
So we add 80 + 8 = 88
Finally 84 : 88
Divide it by 4.
And We get 21 : 22.

Simply find 20% of 7 and 10% of 8.

It will be 1.4 and 0.8 respectively.
Till this ok then,how 8.4:8.8.
And how to convert it into fraction.
So the ratio is 8.4:8.8.

Then convert the fraction into whole numbers.

If I multiply by 10 I will get 84:88 now we can easily simplify it.

So we get 21:22.

Given boys : girls = 7 : 8.

20% of increase in boys i.e 7 becomes 8.4( 10% of 7 means 0.7 therefore, 20% of 7 means 1.4, so we have to add 1.4 to 7)
And then 10% of 8 is 0.8 => girls = 8.8,
8.4 : 8.8 => 84/10 : 88/10.
=>84 : 88.
Further solved into 21: 22 (4 table)..

Hi all,

One minor doubt, why we are using for every question for ratio, what x mean? is a assumed value or what ? for this question if we didn't use x also we are getting the answer, but in other cases, we need to use X, please suggest me a good method.

Thanks.

Let the boys be 7x and girls be 8x.

Boys 20 percent = 7x * 20/100 = 7X/5.
Girls 10 percent = 8x * 10/100 = 4x/5.
Total boys = 7X + 7x/5 = 42x/5.
Total girls = 8x+ 4x/5 = 44x/5.

So, ratio;

Total boys : total girls = 42x/5 /44x/5 = 22/22 = 21:22.

Simply find 20% of 7 and 10% of 8.

It will be 1.4 and 0.8 respectively.

So the ratio is 8.4:8.8.

Then convert the fraction into whole numbers.

If I multiply by 10 I will get 84:88 now we can easily simplify it.

So we get 21:22.

Boys: Girls.
7:8.

20% increase in boys no. so,

7*20% = 1.4 so total boys = 7+1.4 = 8.4.

10% increase in girls.

8*10% = 0.8 So total Girls = 8+0.8 = 8.8.

So Ratio of Boys & Girls.
8.4 : 8.8.

21:22 Answer.