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:a)20b)30c)48d)58Correct answer is option 'B'. Can you explain this answer?

Question

Answer

**Given Information:**
- The sum of three numbers is 98.
- The ratio of the first number to the second number is 2:3.
- The ratio of the second number to the third number is 5:8.

**Let's solve the problem step by step:**

**Step 1:**
Let's assume the three numbers as follows:
- The first number = 2x
- The second number = 3x
- The third number = 8y

**Step 2:**
According to the given information, the sum of the three numbers is 98. Therefore, we can write the equation as:
2x + 3x + 8y = 98

**Step 3:**
Simplifying the equation, we get:
5x + 8y = 98

**Step 4:**
Now, we need to find the values of x and y in order to find the second number.

**Step 5:**
According to the given information, the ratio of the second number to the third number is 5:8. Therefore, we can write the equation as:
3x/8y = 5/8

**Step 6:**
Cross-multiplying the equation, we get:
24x = 40y

**Step 7:**
Simplifying the equation, we get:
3x = 5y

**Step 8:**
Now, we have two equations:
5x + 8y = 98
3x = 5y

**Step 9:**
Substituting the value of 3x from the second equation into the first equation, we get:
5(5y/3) + 8y = 98
25y/3 + 8y = 98
(25y + 24y)/3 = 98
49y/3 = 98
49y = 294
y = 294/49
y = 6

**Step 10:**
Substituting the value of y into the second equation, we get:
3x = 5(6)
3x = 30
x = 30/3
x = 10

**Step 11:**
Now, we can find the second number:
The second number = 3x = 3 * 10 = 30

Therefore, the correct answer is option **B) 30**.

Answer

Let three nubers be x,y,z

x+y+z=98;

x:y = 2:3
=> x/y = 2/3
=> y = 3x/2

y:z = 5:8
=> y/z = 5/8
=> 3x/2z = 5/8
=> 12x= 5z
=> z = 12x/5

x+y+z = 98

substituting y and z values in above eq

x+3x/2+12x/5 = 98

=> (10x+15x+24x)/10= 98

=> 49x = 980

=> x = 20

substitute x value in y & z

y = 3x/2 = 30;

z = 12x/5 = 48;

x= 20; y = 30; z = 48;

Answer

Let 3 parts be A, B, C. Then

A:B=2:3

B:C=5:8

A:B:C=(2x5):(3x5):(3x8)

=10:15:24

Therefore, second no B= [98x15/(10+15+24)]=98x15/49

B=30

Answer

Yr 49 se kse divide kia??

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