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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?
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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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Community 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
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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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