$x:y:z = \frac{1}{2}:\frac{1}{3}:\frac{1}{4}$ 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
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:
