Ratio Numbers Average Difference Calculation
Let the three numbers be $2x$, $3x$, and $5x$, based on the given ratio 2:3:5.
Average Calculation
The average of these three numbers is calculated as:
$ \text{Average} = \frac{2x + 3x + 5x}{3} $
We are given that the average is 100.
$ \frac{10x}{3} = 100 $
Solving for x
To find the value of $x$, we solve the equation:
$ 10x = 100 \times 3 $
$ 10x = 300 $
$ x = \frac{300}{10} $
$ x = 30 $
Finding the Numbers
Now, we find the actual numbers:
- Smallest number: $2x = 2 \times 30 = 60$
- Middle number: $3x = 3 \times 30 = 90$
- Largest number: $5x = 5 \times 30 = 150$
Difference Calculation
The question asks for the difference between the largest and the smallest number.
$ \text{Difference} = \text{Largest Number} - \text{Smallest Number} $
$ \text{Difference} = 150 - 60 $
$ \text{Difference} = 90 $
Similar Questions
If \((x+y):(x-y)=5:2\), find \((x^3+y^3):(x^3-y^3)\)
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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:
