The denominator of a rational number is greater than its numerator by 4. If 1 is added to both the numerator and the denominator, the resulting fraction is \(\dfrac{1}{2}\). Find the rational number.
\(\dfrac{3}{7}\)
A word problem on fractions is solved by naming the unknown numerator, writing the denominator in terms of it, and turning the given condition into a linear equation in one variable.
Step 1 — Let the numerator be \(x\). The denominator is 4 more, so it is \(x + 4\) and the number is \(\dfrac{x}{x+4}\).
Step 2 — Adding 1 to both gives \(\dfrac{x+1}{x+5} = \dfrac{1}{2}\).
Step 3 — Cross-multiply: \(2(x+1) = x + 5\), so \(2x + 2 = x + 5\) and \(x = 3\). The denominator is \(3 + 4 = 7\).
Check — \(\dfrac{3+1}{7+1} = \dfrac{4}{8} = \dfrac{1}{2}\). The fraction \(\dfrac{5}{9}\) becomes \(\dfrac{6}{10}\), \(\dfrac{7}{11}\) becomes \(\dfrac{8}{12}\), and \(\dfrac{1}{5}\) becomes \(\dfrac{2}{6}\), so none of them gives one half.
\(\dfrac{3}{7}\) option is correct.
Similar Questions
The value of the expression \((-3)^3 \times (0.3)^{-2} \times 0.01\) lies between which of the following ranges?
In a class test, a student earns 3 marks for every correct answer and loses 2 marks for every incorrect answer. No marks are given for questions left unattempted. If Radhika scored 20 marks and had 12 correct answers, how many questions did she attempt incorrectly?
If a polyhedron has 6 faces and 12 edges, what is the number of its vertices?
If \(a\) and \(b\) are positive integers (where \(b \neq 0\)) such that \(a^b = 1331\), then what is the value of \((a+b)^{a-b-8}\)?
Numbers that can be expressed as the sum of two cubes in two different ways are known as:
If \(x + \dfrac{y}{2} = \dfrac{1}{4}\), \(y + \dfrac{z}{2} = \dfrac{1}{4}\) and \(z + \dfrac{x}{2} = \dfrac{1}{4}\), then what is the value of \(x + y + z\)?
ABCD is a rhombus in which \(\angle BAC = 50^\circ\). What is the value of \(3\angle D - 2\angle DAC\)?
What is the value of \(\dfrac{\sqrt{450}}{\sqrt{338}} \div \dfrac{\sqrt{125}}{\sqrt{245}}\)?
The selling price of a toy is Rs. 1,020. If the profit made by the shopkeeper is 20%, what is the cost price of the toy?
The sum of two vertically opposite angles \(x\) and \(y\) is 80°. If \(z\) is the complement of \(y\), what is the value of \(3x - y + z\)?
Important Questions from Mixed Topic (JTET)
What type of process is thinking ?
The normal cause of origin of motivation is
How is impulse important for a teacher ?
The motive which forms due to social ideals, status, relations etc. is called
The learning in children starts from
