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
- ₹28,000 were divided among A, B and C, such that 2 times the share of A = 9 times the share of B = 6 times the share of C. Find the share of A.
- Which of the following ratios is the greatest?
- The ratio of the incomes of Barun and Anil is $12 : 13$ and that of their expenditures is $10 : 13$. Find the income of Barun and Anil, if they save $₹2100$ and $₹1,300$, respectively.
- What is the simplest form of the ratio of $6\text{ h} : 3\text{ days}$?
- Two natural numbers are in the ratio of $6 : 8$ and their product is $768$. The smaller of the numbers is:
- Two numbers are in the ratio 2 : 3; if 20 is added to 20% of the smaller number, it will be equal to 10% of the larger number plus 25. Then, the smaller number is: _______.
- The ratio of income of Aamir to that of Ali is 5 : 3 and they expend in the ratio of 9 : 5 respectively. If Aamir saves ₹2,600 and Ali saves ₹1,800, Then their respective incomes are:
- If A : B = 3 : 5 and B : C = 4 : 7, then the value of A : B : C is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
- If the third proportional of 25 and 35 be x, then what is the value of x?
Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
