Question

Anand's income is \(₹ 140\) more than Biren's income and Chandu's income is \(₹ 80\) more than Deepak's. If the ratio of Anand's \& Chandu's income is \(2:3\) and the ratio of Biren's and Deepak's income is \(1:2\), then the incomes of Anand, Biren, Chandu and Deepak are respectively:

• A. \(₹ 260, ₹ 120, ₹ 320 \text{ and } ₹ 240\)
• B. \(₹ 300, ₹ 160, ₹ 600 \text{ and } ₹ 520\)
• C. \(₹ 400, ₹ 260, ₹ 600 \text{ and } ₹ 520\)
• D. \(₹ 320, ₹ 180, ₹ 480 \text{ and } ₹ 360\)

Hint:

In multiple-choice questions, verify the options quickly. For option (C): \(400-260 = 140\), \(600-520 = 80\), \(400:600 = 2:3\), and \(260:520 = 1:2\). All conditions are met.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We represent the income of each person with a variable and set up a system of linear equations based on the given ratios and differences.
Step 2: Key Formula or Approach:
Let incomes be \(A, B, C, D\).
1. \(A = B + 140\)
2. \(C = D + 80\)
3. \(\frac{A}{C} = \frac{2}{3}\)
4. \(\frac{B}{D} = \frac{1}{2} \implies D = 2B\)
Step 3: Detailed Explanation:
Substitute \(D = 2B\) into equation (2):
\[ C = 2B + 80 \]
Now we have \(A = B + 140\) and \(C = 2B + 80\). Substitute these into the ratio equation (3):
\[ \frac{B + 140}{2B + 80} = \frac{2}{3} \]
\[ 3(B + 140) = 2(2B + 80) \]
\[ 3B + 420 = 4B + 160 \]
\[ 4B - 3B = 420 - 160 \implies B = 260 \]
Calculate other values:
\(A = 260 + 140 = 400\)
\(D = 2 \times 260 = 520\)
\(C = 520 + 80 = 600\)
Incomes are \(A=400, B=260, C=600, D=520\).
Step 4: Final Answer:
The incomes of Anand, Biren, Chandu, and Deepak are \(₹ 400, ₹ 260, ₹ 600 \text{ and } ₹ 520\).