A fraction becomes \(1\over2\) if 2 is added to the numerator and 5 is added to the denominator. It also becomes \(1\over 3\) if 2 is subtracted from both the numerator and denominator. The positive difference between the numerator and the denominator is:
2
The correct answer is option 2 i.e. 2.
Let the fraction be \(\dfrac{x}{y}\).
From the conditions, solving the two linear equations gives \(x = 2\).
Hence option (2).
Similar Questions
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
- If a + b = 7 and ab = 12, then \(a^2 + b^2\) is equal to:
Reduce to linear form
\(\frac{5x + 1}{2x} = \frac{5}{4}\)
The value of (x - y)(x + y) + (y - z)(y + z) + (z - x)(z + x) is:
What is the product of (x + a) and (x + b)?
A 3-digit number is such that the units' digit, the tens' digit, and the hundreds' digit are in the ratio 1 : 2 : 3. The sum of this number and the number obtained by writing its digits in reverse order is 1332. Find the number.
- If \(a^2 + b^2 + c^2 + 189 = 6(a + 4b + 2c)\), then \(\sqrt{ab + bc + ca}\) is equal to:
- When the one-third of a number is increased by 83, the result is 97. Find the sum of the digits of the original number.
The cost of 12 pens and 7 pencils is ₹233. If the cost of a pen decreases by ₹1.50 and the cost of a pencil increases by ₹1, then the cost of 2 pens and 3 pencils is ₹48. What is the original cost of 2 pens and 3 pencils?
Important Questions from Algebric Equations
- For what value of K is the equation \(\frac{0.009}{K} = 0.1\) true?
- Arnab buys 9 oranges and 8 bananas for ₹276. When the cost of an orange is decreased by 10% and that of a banana remains the same, then the cost of 5 oranges and 10 bananas is ₹210. What is the original cost of 4 oranges and 3 bananas?
- Find the value of x satisfying: $5(5x^2 - 5) - 5(5x^2 + 7x - 2) = 14$
- The product of two positive numbers is 3645. If the first number is five times the second number, then the sum of the two numbers is:
- The product of two positive numbers is 80. If the first number is five times of the second number, then the sum of the two numbers is:
