Aptitude - Ratio and Proportion - Discussion

@All.

It's Easy to solve it you just need to follow these steps:

Take f as first and s as second and t as third

F:S = 2:3, S:T = 5:8.
We use here some trick of a ratio where we just add the same number after the blank area for example if there is 3 we will write three on 3 front blank area

2 : 3 : 3
5 : 5 : 8.

Multiple it then we get,
10 : 15 : 24.

We sum all three of them we get 49 and the Second person only has 15 per cent so we make it 15/49.Dear @All,

To solve the problem, please follow these simple steps:

1. Let's consider the first value as 'f', the second value as 's', and the third value as 't'.
2. We are given that F:S = 2:3 and S:T = 5:8.
3. To solve this problem, we use a trick of the ratio where we add the same number to the blank area. For example, if there is a blank space of 3, we will write three on the front blank area.
4. Let's apply this trick here. We get the following ratios:
2 : 3 : 3
51 : 5 : 8
5. Now, let's multiply them. We get:
10 .. : 15 : 24
6. Sum all three values. We get 49.
7. The second value is 15, which is 15/49 of the total sum.
8. Let's multiply this with the total sum of 98.
9. The answer is 30.

Then we multiply it by 98 total sums,

98 * 15/49 = 30 answer.
I hope this explanation helps you solve the problem.

let the 3 numbers be x,y,z.

Given is x:y = 2:3 and y:z = 5:8.

So from here we see that y is the common term in both the ratio.

When we will do now is make the value of "y" same in both the ratio.
so in the first ratio, we will multiply the x:y with 5 and the new ratio of x:y will become x:y = 10:15.

And similarly, in the second ratio, we will multiply the y:z with 3 and the new ratio of y:z will become y:z = 15:24
now from the above two newly formed ratio we see that the value of y is the same that is 15.

So from here, we can write the final ratio or proportion of x:y:z as 10:15:24.

So according to the given question, the sum of ratios of x,y,z is 98.

Threrefore, we can write: 10n + 15n + 24n = 98.
=> 49n =98,
=> n = 2,
Thus value of y(the second term) is = 15 n = 15 * 2 = 30.

Instead of doing as per some formula you can solve this question right from the options given below let me explain,

See the question " If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8 ".

* They are asking the value of B only so whose part is 3 and 5 so if you look into the option only the number 30 will be divided by both 3 and 5 whereas other option can't just try with this method it may be useful to you.

CROSS CHECKING THE ANSWER : If B is 30 then A will be 20 and C will be 48 so by adding this (20 + 30 + 48 = 98).

Solution correct !

Given :
A:B = 2:3,
B:C = 5:8,
Ratio of A+B +C = 98.

Solution:
A B C.
2 3 -> 3.
5 <- 5 8.
__________
10 15 24 ( got it by multiply colomn).
___________

Now the ratio of A: B : C is 10: 15: 24.
To convert any Ratio into values multiply by X.
And also from given questions.
10X + 15X + 24 X = 98,
49X = 98,
X = 2,

To find B value from the new ratio of B i.e 15X.
B= 15X,
B = 15(2),
B= 30.

General formula

A:B
B:C
---------------
A*B : B*B : B*C
----------------
A*B + B*B + B*C = sum

Then total should be divided with this sum

Ans = total / sum

This ans should be multiplied with each ratios to get a desired number

In the same way

2:3
5:8
-------
10:15:24 (2*5 : 3*15 : 3*8)

Then adding 10+15+24 gives 49

This 49 divides 98

98 / 49 = 2

B = 2*15 = 30

Similarly

A = 2 * 10 = 20

C = 2 * 24 = 48

Let Assume,

A + B + C = 98

The ratio of the first to second is 2 :3,
Second to the third is 5 : 8.

That Time we Should be Equal the Common Ratio,
Here B is Common Ration.

so, First : Second = (2:3)*5 = 10:15.
Second:Third = (5:8)*3 = 15:24.

Final Ration First:Second:Third = 10:15:24 = 49.

Ratio = (Second Number Ratio / Total Ratio) * Total Amount.
Second Number = (15/49)/98.

Second Number = 30.

Given:

x+y+z = 98.

x:y = 2:3 and y:z = 5:8.

y = ?

Here x:y = 2:3 => x/y = 2/3 => y = (3/2)x = 3x/2 (in form of x.clear).

Similarly, y:z = 5:8 => y/z = 5/8 => z = (8/5) y = 8/5*(3x/2) = 12x/5 (in form of x.clear).

According to question, x+y+z = 98.

So, x+3x/2=12x/5 = 98.

=> 49x/10 = 98.
=> 49x = 980.
=> x = 20.

The value of y = 3x/2 = (3*20)/2 = 30...(Ans).

A B C
2 3 3
5 5 8

Now, new ratio is 10:15:24.

According to the question, the sum of three (10 parts + 15 parts + 24 parts) numbers is 98.
Similarly, (10+15+24) parts = 98.
or, 49 parts = 98.
or, 1 part = 2.
Finally, the second number is 15 parts.
or, 15*2 = 30 (:1 part = 2).

Hi Guys,

I have a shortcut method like this kind of problems see this
a:b:c can be calculated easily from a:b and b:c just multiply as shown below
a:b
b:c
-------
a*b:b*b:b*c

So from the problem 2:3 is a:b and 5:8 is b:c
2:3
5:8
-------
2*5:3*5:3*8
answer is 10:15:24

Here given is sum of three number is 98.
that is 10+15+24=49
49=98
15=? => (15*98)/49 = 30.

Let the three numbers be A, B, C.

A+B+C=98 ----> (I)
Rate:
A/B=2/3 ---> (ii)
B/C=5/8 ---> (iii)
Therefore from (ii);

B = 3A/2 .

From (iii)
B = 5C/8.

Equating B together
3A/2=5C/8.

Therefore, C = 12A/5.
From (I).

A + 3A/2 + 12A/5 = 98.

Therefore, solving for A:
A = 20.
From B=3A/2;
B = 30.
From C=12A/5;
C = 48.

Therefore;
A = 20;
B = 30;
C = 48.