Ratio Calculation: $(2x + 3y):(x + y)$
We are given the ratio $x:y = 2:5$. This means that for some non-zero constant $k$, we can write:
- $x = 2k$
- $y = 5k$
The problem asks for the ratio $(2x + 3y):(x + y)$. We substitute the expressions for $x$ and $y$ in terms of $k$ into this expression.
Evaluating the Expression
First, calculate the numerator part, $2x + 3y$:
$2x + 3y = 2(2k) + 3(5k)$
$2x + 3y = 4k + 15k$
$2x + 3y = 19k$
Next, calculate the denominator part, $x + y$:
$x + y = 2k + 5k$
$x + y = 7k$
Determining the Final Ratio
Now, form the ratio using the calculated values:
$(2x + 3y):(x + y) = (19k):(7k)$
Since $k$ is a non-zero constant, we can cancel $k$ from both sides of the ratio:
$(19k):(7k) = 19:7$
Therefore, the ratio $(2x + 3y):(x + y)$ is $19:7$.
Similar Questions
- A ribbon is cut into three pieces in the ratio 2:3:5. If the length of the longest piece is 20 cm, what is the total length of the ribbon?
- Three numbers are in the ratio 2:3:5. If their average is 100, what is the difference between the largest and the smallest number?
- Three numbers are such that the second is 150% of the first, and the third is 80% of the second. What is the ratio of the first to the third?
- Three friends share a winning prize in the ratio 2:3:4. If the total prize is Rs. 9000, how much more does the person with the highest share get than the lowest?
- A town has males and females in a ratio of 3:2. After 5 years, the male population increases by 10%, and the female population by 25%. What is the new ratio?
- The weights of three friends are in the ratio 7:8:9. If each gains 5 kg, the new ratio becomes 12:13:14. What is the original weight of the heaviest friend?
- Two numbers are in the ratio 6:5. If the difference between them is 11, find the numbers.
- A bag contains red, blue, and green balls in the ratio 4:5:6. If 6 red balls are removed and 3 green balls are added, the new ratio becomes 2:5:7. How many red balls were originally in the bag?
- A recipe requires 0.625 liters of milk for 5 servings. How many servings can be made with 3.75 liters of milk?
Rs. 640 shared among 8 people. 2 back out. What's new share per person?
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 \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
