Question

An amount of Rs.18000 has to be paid to A and B in the ratio 5 : 4. Then A will get

• A. Rs.9000
• B. Rs.11000
• C. Rs.10000
• D. Rs.8000

Hint:

To find a specific share quickly, multiply the total amount by the target share fraction: \[ Share of A = \frac{5}{9} \times 18000 = 5 \times 2000 = Rs. 10,000

Answer 1

The Correct Option is C

Concept: Ratio sharing problems require dividing a total quantity into proportional parts. If a total sum \(S\) is divided between two parties in the ratio \(x : y\), the total number of equal parts created is given by \((x + y)\). The individual shares can be calculated using the formulas: \[ \text{Share of A} = \left( \frac{x}{x+y} \right) \times S \] \[ \text{Share of B} = \left( \frac{y}{x+y} \right) \times S \]

Step 1: Calculate the total number of parts in the ratio distribution.
The given distribution details are:
• Total financial amount to divide (\(S\)) = Rs. 18,000
• Given allocation ratio (\(A : B\)) = \(5 : 4\) Calculate the sum of the ratio parts: \[ \text{Total ratio units} = 5 + 4 = 9 \text{ units} \]

Step 2: Determine the monetary value of a single ratio unit.
Divide the total sum by the total number of parts: \[ 1 \text{ ratio unit value} = \frac{\text{Total Sum}}{\text{Total ratio units}} = \frac{18000}{9} \] \[ 1 \text{ ratio unit value} = \text{Rs. } 2000 \]

Step 3: Compute the explicit monetary share allocated to A.
Since A's share consists of 5 ratio units, multiply this count by the value of a single unit: \[ \text{Share of A} = 5 \times 2000 \] \[ \text{Share of A} = \text{Rs. } 10,000 \] Hence, person A receives an exact total amount of Rs. 10,000. This matches Option (C).