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The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number
- a)200
- b)120
- c)50
- d)160
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The sum of the three numbers is 370. The first number is 1/4th of the ...
Given:
The sum of the three numbers = 370
The first number = 1/4th of the third number
The ratio of the second number to the third = 3 : 5
Calculation:
According to question
Let, 2nd number = 3X & 3rd number = 5X
And, 1st number = (1/4) × 5X = 5X/4
Now, (5X/4) + 3X + 5X = 370
⇒ (5X/4) + 8X = 370
⇒ 37X/4 = 370
⇒ X
= (370 × 4)/37 = 40The third number = 5 × 40 = 200
∴ Correct answer is 200
Most Upvoted Answer
The sum of the three numbers is 370. The first number is 1/4th of the ...
Given Information:
- Sum of the three numbers is 370
- First number is 1/4th of the third number
- Ratio of the second number to the third number is 3:5
Solution:
Step 1: Setting up equations
Let the three numbers be x, y, and z.
From the given information, we can form the following equations:
1. x + y + z = 370
2. x = z/4
3. y/z = 3/5
Step 2: Solving the equations
Substitute the value of x from equation 2 into equation 1:
z/4 + y + z = 370
Rearranging the equation:
y = 370 - z - z/4
y = 370 - 5z/4
Substitute the ratio of y to z from equation 3:
(370 - 5z/4)/z = 3/5
370z - 5z^2 = 12z
Rearranging the equation:
5z^2 - 12z + 370z = 0
5z^2 - 12z + 370z = 0
z(5z - 12 + 370) = 0
5z^2 + 358z = 0
z(5z + 358) = 0
From this equation, we get z = 0 (not possible) or z = 200
Step 3: Finding other numbers
Substitute z = 200 into y = 370 - 5z/4:
y = 370 - 5(200)/4
y = 370 - 250
y = 120
Now, find x using x = z/4:
x = 200/4
x = 50
Therefore, the third number is 200, which is option A.
- Sum of the three numbers is 370
- First number is 1/4th of the third number
- Ratio of the second number to the third number is 3:5
Solution:
Step 1: Setting up equations
Let the three numbers be x, y, and z.
From the given information, we can form the following equations:
1. x + y + z = 370
2. x = z/4
3. y/z = 3/5
Step 2: Solving the equations
Substitute the value of x from equation 2 into equation 1:
z/4 + y + z = 370
Rearranging the equation:
y = 370 - z - z/4
y = 370 - 5z/4
Substitute the ratio of y to z from equation 3:
(370 - 5z/4)/z = 3/5
370z - 5z^2 = 12z
Rearranging the equation:
5z^2 - 12z + 370z = 0
5z^2 - 12z + 370z = 0
z(5z - 12 + 370) = 0
5z^2 + 358z = 0
z(5z + 358) = 0
From this equation, we get z = 0 (not possible) or z = 200
Step 3: Finding other numbers
Substitute z = 200 into y = 370 - 5z/4:
y = 370 - 5(200)/4
y = 370 - 250
y = 120
Now, find x using x = z/4:
x = 200/4
x = 50
Therefore, the third number is 200, which is option A.
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The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer?
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The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer?.
The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer? for Software Development 2025 is part of Software Development preparation. The Question and answers have been prepared according to the Software Development exam syllabus. Information about The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for Software Development 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The sum of the three numbers is 370. The first number is 1/4th of the third number, and the ratio of the second number to the third is 3 : 5. Find the third number a)200b)120c)50d)160Correct answer is option 'A'. Can you explain this answer?.
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