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The sum of 3 numbers is 285. Ratio between 2nd and 3rd numbers is 6 ∶ 5. Ratio between 1st and 2nd numbers is 3 ∶ 7. The 3rd number is?
- a)135
- b)150
- c)124
- d)105
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
The sum of 3 numbers is 285. Ratio between 2nd and 3rd numbers is 6 5...
Given:
The sum of 3 numbers is 285. Ratio between 2nd and 3rd numbers is 6 ∶ 5.
Ratio between 1st and 2nd numbers is 3 ∶ 7.
Calculation:
Let the 1st number be x
Let the 2nd number be y
Let the 3rd number be z
The sum of 3rd number is 285
According to the question
Ratio of 2nd and 3rd number
⇒ y : z = 6 : 5
Ratio of 1th and 2nd number
⇒ x : y = 3 : 7
Ratio of x : y : z
⇒ (x × y) : (y × y) : (y × z) = (3 × 6) : (7 × 6) : (7 × 5)
⇒ x : y : z = 18 : 42 : 35
The 3rd number z = 285 × 35 /(18 + 42 + 35)
⇒ z = 285 × 35 / 95 = 105
∴ The 3rd number is 105
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Community Answer
The sum of 3 numbers is 285. Ratio between 2nd and 3rd numbers is 6 5...
Understanding the Problem
We have three numbers, and their sum is 285. We also have two ratios that relate these numbers:
1. The ratio of the 2nd to the 3rd number is 6:5.
2. The ratio of the 1st to the 2nd number is 3:7.
Setting Up the Variables
Let's denote the three numbers as:
- 1st number = A
- 2nd number = B
- 3rd number = C
From the ratios, we can express B and C in terms of a variable:
- Since B:C = 6:5, we can express B as 6x and C as 5x for some variable x.
- Since A:B = 3:7, we can express A as (3/7)B = (3/7)(6x) = 18x/7.
Summing Up the Numbers
According to the problem, the sum of the numbers is:
A + B + C = 285
Substituting the values:
(18x/7) + 6x + 5x = 285
To combine these, we need a common denominator:
(b) 18x/7 + (42x/7) + (35x/7) = 285
(b) (18x + 42x + 35x) / 7 = 285
(b) 95x / 7 = 285
Now, multiplying both sides by 7:
(b) 95x = 1995
Now, solving for x:
(b) x = 1995 / 95 = 21
Finding the Values of Each Number
Now we can find each number:
- C = 5x = 5 * 21 = 105
- B = 6x = 6 * 21 = 126
- A = 18x/7 = 18 * 21 / 7 = 54
Conclusion
Thus, the 3rd number, C, is 105, which corresponds to option 'D'.
We have three numbers, and their sum is 285. We also have two ratios that relate these numbers:
1. The ratio of the 2nd to the 3rd number is 6:5.
2. The ratio of the 1st to the 2nd number is 3:7.
Setting Up the Variables
Let's denote the three numbers as:
- 1st number = A
- 2nd number = B
- 3rd number = C
From the ratios, we can express B and C in terms of a variable:
- Since B:C = 6:5, we can express B as 6x and C as 5x for some variable x.
- Since A:B = 3:7, we can express A as (3/7)B = (3/7)(6x) = 18x/7.
Summing Up the Numbers
According to the problem, the sum of the numbers is:
A + B + C = 285
Substituting the values:
(18x/7) + 6x + 5x = 285
To combine these, we need a common denominator:
(b) 18x/7 + (42x/7) + (35x/7) = 285
(b) (18x + 42x + 35x) / 7 = 285
(b) 95x / 7 = 285
Now, multiplying both sides by 7:
(b) 95x = 1995
Now, solving for x:
(b) x = 1995 / 95 = 21
Finding the Values of Each Number
Now we can find each number:
- C = 5x = 5 * 21 = 105
- B = 6x = 6 * 21 = 126
- A = 18x/7 = 18 * 21 / 7 = 54
Conclusion
Thus, the 3rd number, C, is 105, which corresponds to option 'D'.
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