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In a fraction X, if thrice the denominator is decreased by 30% and twice the numerator is increased by 10%, then the resultant fraction is 22% of 26/21. Find the fraction X.
- a)4/25
- b)13/50
- c)3/25
- d)13/5
Correct answer is option 'B'. Can you explain this answer?
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Most Upvoted Answer
In a fraction X, if thrice the denominator is decreased by 30% and twi...
Let the fraction X be x/y.
Hence, option (2) is the correct answer.
Hence, option (2) is the correct answer.
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Community Answer
In a fraction X, if thrice the denominator is decreased by 30% and twi...
To solve this problem, let's first understand the given information step by step.
Step 1: Understand the given information
- We have a fraction X, with a numerator and a denominator.
- The numerator is multiplied by 2 and increased by 10%.
- The denominator is multiplied by 3 and decreased by 30%.
- The resulting fraction is equal to 22% of 26/21.
Step 2: Express the given information mathematically
Let's assume the original fraction X as a/b, where a is the numerator and b is the denominator.
According to the given information:
- The new numerator is 2a + 10% of 2a, which can be written as 2a + 0.1(2a) = 2a + 0.2a = 2.2a.
- The new denominator is 3b - 30% of 3b, which can be written as 3b - 0.3(3b) = 3b - 0.9b = 2.1b.
- The resulting fraction is 22% of 26/21, which can be written as 0.22 * (26/21).
So, the equation becomes:
(2.2a) / (2.1b) = 0.22 * (26/21).
Step 3: Solve the equation
To solve the equation, let's simplify it by canceling out common factors:
(2.2/2.1) * a/b = 0.22 * (26/21).
(22/21) * a/b = (26/100) * (26/21).
(22/21) * a/b = (26^2)/(21 * 100).
(22/21) * a/b = (676)/(2100).
Now, let's cross multiply:
22 * (676) * b = 21 * (2100) * a.
Simplifying further:
b = (21 * 2100 * a) / (22 * 676).
b = (21/22) * (2100/676) * a.
Step 4: Find the value of a/b
Since we need to find the fraction X, we need to find the value of a/b. From the equation above, we can see that b is dependent on a.
To simplify things, let's assume a = 1. This means:
b = (21/22) * (2100/676) * 1.
b = (21/22) * (100/169).
b = (21 * 100) / (22 * 169).
b = 2100 / 3698.
b ≈ 0.567.
Therefore, the fraction X is approximately 1/0.567, which can be simplified to 13/50. Hence, the correct answer is option B) 13/50.
Step 1: Understand the given information
- We have a fraction X, with a numerator and a denominator.
- The numerator is multiplied by 2 and increased by 10%.
- The denominator is multiplied by 3 and decreased by 30%.
- The resulting fraction is equal to 22% of 26/21.
Step 2: Express the given information mathematically
Let's assume the original fraction X as a/b, where a is the numerator and b is the denominator.
According to the given information:
- The new numerator is 2a + 10% of 2a, which can be written as 2a + 0.1(2a) = 2a + 0.2a = 2.2a.
- The new denominator is 3b - 30% of 3b, which can be written as 3b - 0.3(3b) = 3b - 0.9b = 2.1b.
- The resulting fraction is 22% of 26/21, which can be written as 0.22 * (26/21).
So, the equation becomes:
(2.2a) / (2.1b) = 0.22 * (26/21).
Step 3: Solve the equation
To solve the equation, let's simplify it by canceling out common factors:
(2.2/2.1) * a/b = 0.22 * (26/21).
(22/21) * a/b = (26/100) * (26/21).
(22/21) * a/b = (26^2)/(21 * 100).
(22/21) * a/b = (676)/(2100).
Now, let's cross multiply:
22 * (676) * b = 21 * (2100) * a.
Simplifying further:
b = (21 * 2100 * a) / (22 * 676).
b = (21/22) * (2100/676) * a.
Step 4: Find the value of a/b
Since we need to find the fraction X, we need to find the value of a/b. From the equation above, we can see that b is dependent on a.
To simplify things, let's assume a = 1. This means:
b = (21/22) * (2100/676) * 1.
b = (21/22) * (100/169).
b = (21 * 100) / (22 * 169).
b = 2100 / 3698.
b ≈ 0.567.
Therefore, the fraction X is approximately 1/0.567, which can be simplified to 13/50. Hence, the correct answer is option B) 13/50.
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