Three numbers are in the ratio \(\dfrac{4}{8} : \dfrac{11}{16} : \dfrac{18}{21}\). The difference between the largest and the smallest number is 40. Find the largest of the three numbers.
96
The given ratio is \(\dfrac{4}{8} : \dfrac{11}{16} : \dfrac{18}{21}\). Take the LCM of the denominators 8, 16 and 21, which is 336.
Convert each fraction to the common denominator 336: \(\dfrac{4}{8} = \dfrac{168}{336}\), \(\dfrac{11}{16} = \dfrac{231}{336}\), \(\dfrac{18}{21} = \dfrac{288}{336}\).
So the numbers are in the ratio 168 : 231 : 288. The largest part is 288 and the smallest is 168.
Let the numbers be 168k, 231k and 288k. Difference of largest and smallest \(= 288k - 168k = 120k\).
Given \(120k = 40\), so \(k = \dfrac{40}{120} = \dfrac{1}{3}\).
Largest number \(= 288k = 288 \times \dfrac{1}{3} = 96\).
Hence, the largest of the three numbers is 96.
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
