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The sum of three numbers is 98. The ratio of the first two numbers is 2 : 3 and that of the last two numbers is 5 : 8. Find the 2nd number.
- a)48
- b)30
- c)20
- d)15
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
The sum of three numbers is 98. The ratio of the first two numbersis 2...
Let the numbers be x, y and z.
x + y + z = 98
Also, x : y = 2 : 3 and
Therefore, x : y : z = 10 : 15 : 24
Let x = 10k, y = 15k and z = 24k
Then, 10k + 15k + 24k = 98
⇒
x + y + z = 98
Also, x : y = 2 : 3 and
y
: z = 5 : 8Therefore, x : y : z = 10 : 15 : 24
Let x = 10k, y = 15k and z = 24k
Then, 10k + 15k + 24k = 98
⇒
k = 2
The numbers are 20, 30 and 48.
Hence, second number is 30.
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Community Answer
The sum of three numbers is 98. The ratio of the first two numbersis 2...
Understanding the Problem
We have three numbers, let's denote them as A, B, and C. The problem provides us with the following information:
- The sum of the numbers: A + B + C = 98
- The ratio of the first two numbers: A : B = 2 : 3
- The ratio of the last two numbers: B : C = 5 : 8
Finding the Values of A, B, and C
1. Express A and B in terms of a common variable
Since A : B = 2 : 3, we can write:
- A = 2x
- B = 3x
2. Express B and C in terms of another variable
From the ratio B : C = 5 : 8, we can write:
- B = 5y
- C = 8y
3. Equate B from both expressions
Since both expressions represent B, we can set them equal:
- 3x = 5y
4. Express y in terms of x
Rearranging gives us:
- y = (3/5)x
5. Substituting y back into the expression for C
C can be expressed as:
- C = 8y = 8 * (3/5)x = (24/5)x
Finding the Total Sum
Now, substitute A, B, and C back into the sum equation:
- A + B + C = 2x + 3x + (24/5)x = 98
Combining the terms gives:
- (10x + (24/5)x) = 98
Converting 10x into a fraction:
- (50/5)x + (24/5)x = 98
- (74/5)x = 98
Solving for x
Multiply both sides by 5:
- 74x = 490
- x = 490 / 74 = 6.64 (approximately)
Calculating B
Now, substitute x back to find B:
- B = 3x = 3 * (490 / 74) = 30
Conclusion
Thus, the second number B is 30, confirming that the correct option is (b) 30.
We have three numbers, let's denote them as A, B, and C. The problem provides us with the following information:
- The sum of the numbers: A + B + C = 98
- The ratio of the first two numbers: A : B = 2 : 3
- The ratio of the last two numbers: B : C = 5 : 8
Finding the Values of A, B, and C
1. Express A and B in terms of a common variable
Since A : B = 2 : 3, we can write:
- A = 2x
- B = 3x
2. Express B and C in terms of another variable
From the ratio B : C = 5 : 8, we can write:
- B = 5y
- C = 8y
3. Equate B from both expressions
Since both expressions represent B, we can set them equal:
- 3x = 5y
4. Express y in terms of x
Rearranging gives us:
- y = (3/5)x
5. Substituting y back into the expression for C
C can be expressed as:
- C = 8y = 8 * (3/5)x = (24/5)x
Finding the Total Sum
Now, substitute A, B, and C back into the sum equation:
- A + B + C = 2x + 3x + (24/5)x = 98
Combining the terms gives:
- (10x + (24/5)x) = 98
Converting 10x into a fraction:
- (50/5)x + (24/5)x = 98
- (74/5)x = 98
Solving for x
Multiply both sides by 5:
- 74x = 490
- x = 490 / 74 = 6.64 (approximately)
Calculating B
Now, substitute x back to find B:
- B = 3x = 3 * (490 / 74) = 30
Conclusion
Thus, the second number B is 30, confirming that the correct option is (b) 30.
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