$x:y:z = \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ 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
If the ratio of three numbers A, B and C is 2 ∶ 3 ∶ 5, and the sum of the squares of these numbers is 3800, then the value of C is:
A bag contains ₹310 in the form of 5 rupee, 2 rupee and 1 rupee coins in the ratio 4 ∶ 3 ∶ 5. What is the number of 5 rupee coins?
The ratio of three numbers is 3 ∶ 5 ∶ 4 and the sum of their squares is 11250. Find the sum of the numbers.
When 'x' is subtracted from each of the numbers 22, 39, 56 and 107, then the resulting numbers, in this order, are in proportion. What is the mean proportional between (x + 3) and (3x - 7)?
The salaries of Ravi and Sumit are in the ratio 4 ∶ 5. If the salary of each is increased by Rs. 6,000 the new ratio becomes 35 ∶ 40. What will be Sumit's increased salary?
