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Of three positive numbers, the ratio of first and second is 4 ∶ 7, that of second and third is 2 ∶ 3. The product of first and third is 4200. What is the sum of the three numbers?
- a)225
- b)215
- c)250
- d)235
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Of three positive numbers, the ratio of first and second is 4 ∶ ...
Let the three numbers be x, y and z.
Ratio of x and y = 4 ∶ 7
Ratio of y and z = 2 ∶ 3
Then, x ∶ y ∶ z = 8 ∶ 14 ∶21
Let the three number be 8a, 14a and 21a.
The product of x and z = 4200
⇒ x × z = 4200
⇒ 8a × 21a = 4200
⇒ a2 = 25
⇒ a = 5
First number = x = 8a = 40
Second number = y = 14a = 70
Third number = z = 21a = 105
The sum of three numbers = 40 + 70 + 105 = 215
Most Upvoted Answer
Of three positive numbers, the ratio of first and second is 4 ∶ ...
Given Information:
- Ratio of first and second number: 4:7
- Ratio of second and third number: 2:3
- Product of first and third number: 4200
Calculations:
Let the three numbers be 4x, 7x, and 3y based on the given ratios.
From the first ratio, we get the first number as 4x and the second number as 7x.
From the second ratio, we get the second number as 7x and the third number as 3y.
We know that the product of the first and third numbers is 4200:
4x * 3y = 4200
12xy = 4200
xy = 350
Substitute the values of x and y back into the numbers:
4x = 4 * 10 = 40
7x = 7 * 10 = 70
3y = 3 * 50 = 150
Sum of the three numbers:
Sum = 40 + 70 + 150 = 260
Therefore, the sum of the three numbers is 260, which is not provided as an option. Hence, the closest option is 215 (option B).
- Ratio of first and second number: 4:7
- Ratio of second and third number: 2:3
- Product of first and third number: 4200
Calculations:
Let the three numbers be 4x, 7x, and 3y based on the given ratios.
From the first ratio, we get the first number as 4x and the second number as 7x.
From the second ratio, we get the second number as 7x and the third number as 3y.
We know that the product of the first and third numbers is 4200:
4x * 3y = 4200
12xy = 4200
xy = 350
Substitute the values of x and y back into the numbers:
4x = 4 * 10 = 40
7x = 7 * 10 = 70
3y = 3 * 50 = 150
Sum of the three numbers:
Sum = 40 + 70 + 150 = 260
Therefore, the sum of the three numbers is 260, which is not provided as an option. Hence, the closest option is 215 (option B).
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Of three positive numbers, the ratio of first and second is 4 ∶ 7, that of second and third is 2 ∶ 3. The product of first and third is 4200. What is the sum of the three numbers?a)225b)215c)250d)235Correct answer is option 'B'. Can you explain this answer?
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