If A and B together earn Rs. 900 in an hour and A's share is half of B's share, then B's share is?
Understand the Problem
The question is asking to determine B's share of earnings given that A and B together earn Rs. 900 and that A's share is half of B's share. It requires understanding of ratios and basic arithmetic to solve it.
Answer
B's share is $600$.
Answer for screen readers
B's share is $600$.
Steps to Solve
- Define Variables
Let B's share be denoted as $B$. According to the problem, A's share is half of B's share, so we can denote A's share as $A = \frac{1}{2}B$.
- Set Up the Equation
Since A and B together earn Rs. 900, we can set up the equation:
$$ A + B = 900 $$
Substituting for $A$:
$$ \frac{1}{2}B + B = 900 $$
- Combine Terms
Combine the terms on the left side of the equation:
$$ \frac{1}{2}B + \frac{2}{2}B = 900 $$
This simplifies to:
$$ \frac{3}{2}B = 900 $$
- Solve for B
To solve for $B$, multiply both sides by $\frac{2}{3}$:
$$ B = 900 \times \frac{2}{3} $$
Calculating this gives:
$$ B = 600 $$
- Conclusion
Thus, B's share is Rs. 600.
B's share is $600$.
More Information
In this problem, we utilized the concepts of ratios and basic algebra to find the shares of A and B in the total earnings. Understanding how to express relationships with variables is critical in problem-solving.
Tips
- Failing to correctly set up the equation based on the relationship between A and B can lead to incorrect answers.
- Miscalculating the total or individual shares when solving can occur if the fractions are not managed properly.
