Aptitude - Ratio and Proportion - Discussion
Discussion Forum : Ratio and Proportion - General Questions (Q.No. 9)
9.
The sum of three numbers is 98. If the ratio of the first to second is 2 :3 and that of the second to the third is 5 : 8, then the second number is:
Answer: Option
Explanation:
Let the three parts be A, B, C. Then,
| A : B = 2 : 3 and B : C = 5 : 8 = |  |
5 x | 3 |  |
: | |
8 x | 3 | |
= 3 : | 24 |
| 5 | 5 | 5 |
 A : B : C = 2 : 3 : |
24 | = 10 : 15 : 24 |
| 5 |
| B = |
|
98 x | 15 | |
= 30. |
| 49 |
Discussion:
122 comments Page 5 of 13.
Deva said:
1 decade ago
Please tell me the easy way to solve this problem?
Abhijith said:
1 decade ago
x+y+z = 98;--> eq.1
x/y = 2/3;
y/z = 5/8;
x = (2y/3);
z = (8y/5).
Substituting new value of x and z in eq 1,
=> (2y/3)+y+(8y/5)=98;
Taking LCM as 15;
=> (10y+15y+24y)/15=98;
=> 49y=98*15;
=> y=(98*15)/49;
=> y=2*15;
=> y=30.
x/y = 2/3;
y/z = 5/8;
x = (2y/3);
z = (8y/5).
Substituting new value of x and z in eq 1,
=> (2y/3)+y+(8y/5)=98;
Taking LCM as 15;
=> (10y+15y+24y)/15=98;
=> 49y=98*15;
=> y=(98*15)/49;
=> y=2*15;
=> y=30.
Shipra said:
1 decade ago
Hello guys!
There is a short trick for these kinds of questions.
Given,
A:B = 2:3.
B:C = 5:8.
Multiply A and B (below one) , B and B (below one) and lastly B and C (below one).
We directly get 10:15:24.
Now add them all i.e. (10+15+24) = 49.
From formula,
(98*15)/49 = 30.
There is a short trick for these kinds of questions.
Given,
A:B = 2:3.
B:C = 5:8.
Multiply A and B (below one) , B and B (below one) and lastly B and C (below one).
We directly get 10:15:24.
Now add them all i.e. (10+15+24) = 49.
From formula,
(98*15)/49 = 30.
Jayadev samantaray said:
1 decade ago
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).
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).
MANDEEP SINGH said:
1 decade ago
A:B:C.
2:3.
5:8.
We get A:B:C.
A = 2X5 = 10;
B = 3X5 = 15;
C = 3X8 = 24;
A:B:C = 10:15:24.
10x+15x+24x = 98.
49x = 98.
x = 2.
So B's sum is: 15X2 = 30.
2:3.
5:8.
We get A:B:C.
A = 2X5 = 10;
B = 3X5 = 15;
C = 3X8 = 24;
A:B:C = 10:15:24.
10x+15x+24x = 98.
49x = 98.
x = 2.
So B's sum is: 15X2 = 30.
Swagger said:
1 decade ago
The easiest way:
a:b:c.
2:3.
5:8.
So 8/5 = 1.6. So c is 1.6 times bigger than b.
So 3*1.6 = 24/5.
Therefore, the ratio is 2:3:24/5.
Simplifying gives ratio as 10:15:24.
To solve the question 10x:15x:24x = 98.
10x+15x+24x = 98,
So 49x = 98, x=2.
Therefore the second number is 15*2 = 30.
a:b:c.
2:3.
5:8.
So 8/5 = 1.6. So c is 1.6 times bigger than b.
So 3*1.6 = 24/5.
Therefore, the ratio is 2:3:24/5.
Simplifying gives ratio as 10:15:24.
To solve the question 10x:15x:24x = 98.
10x+15x+24x = 98,
So 49x = 98, x=2.
Therefore the second number is 15*2 = 30.
Muhammad Usman Shoaib said:
10 years ago
If are is the remainder when a positive integer is divided by a single- digit prime integer, what is the largest possible value of are?
Options : A 6, B 7, C 8, D 9 and E : It cannot be determined from the information above.
Options : A 6, B 7, C 8, D 9 and E : It cannot be determined from the information above.
Guru said:
10 years ago
Why should take 8?
Bhuvana said:
10 years ago
@Sid.
How can you say total 150 members?
How can you say total 150 members?
ADITYA JAIN said:
9 years ago
Let the three ratio be = A:B:C.
A:B = 2:3.
B:C = 5:8.
Now A:B:C = 10:15:24 (2*5 = 10, 3*5 = 15, 3*8 = 24).
Now 10 + 15 + 24 = 49.
B = 98 * 15/49.
= 30.
A:B = 2:3.
B:C = 5:8.
Now A:B:C = 10:15:24 (2*5 = 10, 3*5 = 15, 3*8 = 24).
Now 10 + 15 + 24 = 49.
B = 98 * 15/49.
= 30.
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