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Three numbers are in the ratio 410:2018:2011\frac{4}{10} : \frac{20}{18} : \frac{20}{11}104​:1820​:1120​​. The difference between the greatest and the
Question

Three numbers are in the ratio 410:2018:2011\frac{4}{10} : \frac{20}{18} : \frac{20}{11}​. The difference between the greatest and the smallest numbers is 39. Find the largest number.

A.

51

B.

49

C.

48

D.

50

Correct option is D

Given
Ratio of three numbers = 410:2018:2011\frac{4}{10} : \frac{20}{18} : \frac{20}{11}​​
Difference between the greatest and smallest numbers = 39
Formula Used
Difference = Greatest value - Smallest value

Solution
Simplify the given ratio fractions:
25:109:2011\frac{2}{5} : \frac{10}{9} : \frac{20}{11}​​
To remove fractions, find the LCM of denominators 5, 9, and 11, which is 5×9×11=4955 \times 9 \times 11 = 495​.
Multiply each term by 495:
25×495=198 109×495=550 2011×495=900\frac{2}{5} \times 495 = 198 \\\ \\\frac{10}{9} \times 495 = 550 \\\ \\\frac{20}{11} \times 495 = 900​​
The simplified ratio is 198 : 550 : 900.
Dividing by their common factor 2:
99 : 275 : 450.
Let the numbers be 99x, 275x, and 450x.
The greatest number is 450x and the smallest is 99x.
According to the given condition:
450x - 99x = 39
351x = 39
x=39351=19x = \frac{39}{351} = \frac{1}{9}​​
The largest number is 450x:
Largest number = 450×19=50450 \times \frac{1}{9} = 50​​
Final Answer
So the correct answer is (d)

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