Ratio Calculation: Finding the Greatest Number
The problem asks us to find the greatest number among three numbers that are in a specific ratio and have a given sum.
Representing the Numbers
Let the three numbers be represented using the given ratio $11 : 16 : 23$. We can denote these numbers as $11x$, $16x$, and $23x$, where '$x$' is a common multiplier.
Using the Sum to Find the Multiplier
We are given that the sum of these three numbers is $150$. Therefore, we can set up the equation:
$11x + 16x + 23x = 150$
First, sum the coefficients of '$x$':
$ (11 + 16 + 23)x = 150 $
$ 50x = 150 $
Now, solve for '$x$' by dividing both sides by $50$:
$ x = \frac{150}{50} $
$ x = 3 $
Calculating the Greatest Number
The three numbers are $11x$, $16x$, and $23x$. The greatest number corresponds to the largest part of the ratio, which is $23$. To find the value of the greatest number, substitute the value of '$x$' ($x=3$) into the expression for the greatest number:
Greatest Number = $23x$
Greatest Number = $23 \times 3$
Greatest Number = $69$
Thus, the greatest number among the three is $69$.
Similar Questions
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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:
