Question

Two friends A and B have decided to donate a sum of amount to a government school in the ratio 2 : 3. If B has donated Rs.120000, then the total amount donated by both A and B is

• A. Rs. 180000
• B. Rs. 190000
• C. Rs. 200000
• D. Rs. 220000

Hint:

To save time, use the unit method: 3 units = 120,000. Therefore, 1 unit = 40,000. The total is 5 units ($2+3$). Total = $5 \times 40,000 = 200,000$.

Answer 1

The Correct Option is C

Concept: When a total is divided into a ratio $x:y$, the parts can be represented as $xk$ and $yk$. Here, we are given one part and asked to find the sum of both parts.

Step 1: Define the proportions.
The ratio of donation is $A:B = 2:3$. Let the common multiplier be $k$.
• Amount donated by A = $2k$
• Amount donated by B = $3k$
• Total Amount = $2k + 3k = 5k$

Step 2: Solve for the constant $k$.
We are given that B donated Rs. 120,000. \[ 3k = 120000 \] \[ k = \frac{120000}{3} \] \[ k = 40000 \]

Step 3: Calculate the total donation.
Now, substitute the value of $k$ back into the total amount expression: \[ \text{Total} = 5k \] \[ \text{Total} = 5 \times 40000 \] \[ \text{Total} = 200000 \] The total amount donated by both friends is Rs. 2,00,000. Final Answer: Option C