$x:y:z = \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ What is the value of $\frac{x+z-y}{y}$?
Ratio Simplification
The given ratio is $x:y:z = \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$.
- To simplify the ratio, find the least common multiple (LCM) of the denominators (2, 3, and 4). The LCM is 12.
- Multiply each fraction in the ratio by the LCM:
- $x = \frac{1}{2} \times 12 = 6$
- $y = \frac{1}{3} \times 12 = 4$
- $z = \frac{1}{4} \times 12 = 3$
- The simplified ratio is $x:y:z = 6:4:3$.
Expression Evaluation
We need to find the value of the expression $\frac{x+z-y}{y}$.
- Let $x = 6k$, $y = 4k$, and $z = 3k$, where $k$ is a constant.
- Substitute these values into the expression: $ \frac{x+z-y}{y} = \frac{6k + 3k - 4k}{4k} $
- Simplify the numerator: $ \frac{(6+3-4)k}{4k} = \frac{5k}{4k} $
- Cancel out the constant $k$: $ \frac{5}{4} $
- Convert the fraction to a decimal: $ \frac{5}{4} = 1.25 $
The value of the expression $\frac{x+z-y}{y}$ is 1.25.
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 \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
