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Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers?
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Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest...
Understanding the Problem
To solve for three numbers in the ratio 4:5:6, we first express these numbers in terms of a variable, say 'x'. Thus, we have:
- First number = 4x
- Second number = 5x
- Third number = 6x
Setting Up the Equation
According to the problem, the sum of the largest and smallest numbers equals the sum of the third number and 55. Therefore, we can write the equation as:
- (6x + 4x) = (5x + 55)
Simplifying the Equation
Now, simplify the equation:
- 10x = 5x + 55
Subtract 5x from both sides:
- 10x - 5x = 55
- 5x = 55
Finding the Value of x
To find x, divide both sides by 5:
- x = 11
Calculating the Numbers
Now, substitute x back into the expressions for the three numbers:
- First number = 4x = 4 * 11 = 44
- Second number = 5x = 5 * 11 = 55
- Third number = 6x = 6 * 11 = 66
Final Result
Thus, the three numbers are:
- First number: 44
- Second number: 55
- Third number: 66
Verification
To verify, check the condition:
- Largest (66) + Smallest (44) = 110
- Third (55) + 55 = 110
Both sides are equal, confirming our solution is correct.
To solve for three numbers in the ratio 4:5:6, we first express these numbers in terms of a variable, say 'x'. Thus, we have:
- First number = 4x
- Second number = 5x
- Third number = 6x
Setting Up the Equation
According to the problem, the sum of the largest and smallest numbers equals the sum of the third number and 55. Therefore, we can write the equation as:
- (6x + 4x) = (5x + 55)
Simplifying the Equation
Now, simplify the equation:
- 10x = 5x + 55
Subtract 5x from both sides:
- 10x - 5x = 55
- 5x = 55
Finding the Value of x
To find x, divide both sides by 5:
- x = 11
Calculating the Numbers
Now, substitute x back into the expressions for the three numbers:
- First number = 4x = 4 * 11 = 44
- Second number = 5x = 5 * 11 = 55
- Third number = 6x = 6 * 11 = 66
Final Result
Thus, the three numbers are:
- First number: 44
- Second number: 55
- Third number: 66
Verification
To verify, check the condition:
- Largest (66) + Smallest (44) = 110
- Third (55) + 55 = 110
Both sides are equal, confirming our solution is correct.
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Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers?
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Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers?.
Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Three numbers are in ratio 4 ratio 5 ratio 6 if the sum of the largest and the smallest equals the sum of the third and 55 find the numbers?.
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