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If three numbers are in the ratio 5:6:8 and their sum is 3800, then the greatest number will be:
1200
2000
1000
1600
1600
Multiply the total sum by the greatest ratio component and divide by the sum of all ratio components (8/(5+6+8)×3800).
Ratio of three numbers = 5 : 6 : 8, Sum of the numbers = 3800
Greatest Number=Sum of ratiosRatio value of greatest number×Total Sum
Multiply the total sum by the greatest ratio component and divide by the sum of all ratio components (8/(5+6+8)×3800).
Multiplying by the wrong ratio or dividing the sum by the number of items instead of the sum of the ratio parts.
Step 1: Assume the numbers
Since the numbers are in the ratio 5:6:8, let the three numbers be 5x, 6x, and 8x respectively.
5x,6x,8x
Step 2: Set up the equation using the sum
The sum of the three numbers is given as 3800. Therefore, add the algebraic terms and equate to 3800.
5x+6x+8x=3800
Step 3: Solve for x
Combine like terms: 19x=3800. Divide both sides by 19 to find the value of x.
x=193800=200
Step 4: Find the greatest number
The greatest number corresponds to the largest ratio component, which is 8x. Substitute x=200.
Greatest Number=8×200=1600
D is correct because the greatest number is 1600.
Ratio problems frequently appear in partnership, age-related, and mixture problems across competitive exams.
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