Question

Salaries ratio 2:3. After adding Rs.4000 each \(\rightarrow\) ratio 40:57. Find Jimmy's salary.

• A. Rs.34000
• B. Rs.46800
• C. Rs.36700
• D. Rs.50000

Hint:

For ratio problems, assume the quantities as multiples of a common variable (like \(2x\) and \(3x\)). Then form an equation using the changed ratio and solve systematically.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The salaries of two persons are in the ratio \(2:3\). After adding Rs.4000 to each salary, the ratio becomes \(40:57\). We need to find Jimmy's salary.

Step 2: Key Formula or Approach:
If two quantities are in the ratio \(2:3\), they can be written as: \[ 2x \text{ and } 3x \] After adding Rs.4000 to each: \[ \frac{2x+4000}{3x+4000}=\frac{40}{57} \]

Step 3: Detailed Explanation:
Let the original salaries be: \[ 2x \text{ and } 3x \] According to the question: \[ \frac{2x+4000}{3x+4000}=\frac{40}{57} \] Cross multiply: \[ 57(2x+4000)=40(3x+4000) \] Expand both sides: \[ 114x+228000=120x+160000 \] Bring like terms together: \[ 228000-160000=120x-114x \] \[ 68000=6x \] \[ x=\frac{68000}{6}=\frac{34000}{3} \] Now calculate the salaries: \[ 2x=\frac{68000}{3}\approx 22666.67 \] \[ 3x=34000 \] Thus, the larger salary (Jimmy's salary) is: \[ \text{Rs. }34000 \]

Step 4: Final Answer:
Jimmy's original salary is: \[ \boxed{\text{Rs. }34000} \]

Answer 2

The salaries are in the ratio 2:3, and after adding Rs. 4000 to each the ratio becomes 40:57. Since Jimmy's salary is the larger of the two (matching the "3" part of the original ratio), we can check each option by adding Rs. 4000 and seeing whether the resulting ratio to the matching smaller salary works out to 40:57.

1. Rs. 34000: If Jimmy's original salary is 34000, the matching smaller salary (in the ratio 2:3) is \( \frac{2}{3} \times 34000 \approx 22666.67 \). Adding Rs. 4000 to each gives 38000 and about 26666.67, and \( \frac{26666.67}{38000} \approx 0.702 \), which is the same as \( \frac{40}{57} \approx 0.702 \). This matches.
2. Rs. 46800: The matching smaller salary would be \( \frac{2}{3} \times 46800 = 31200 \). Adding Rs. 4000 to each gives 50800 and 35200, and \( \frac{35200}{50800} \approx 0.693 \), which does not equal \( \frac{40}{57} \approx 0.702 \), so this does not fit.
3. Rs. 36700: The matching smaller salary would be \( \frac{2}{3} \times 36700 \approx 24466.67 \). Adding Rs. 4000 to each gives 40700 and about 28466.67, and \( \frac{28466.67}{40700} \approx 0.699 \), which is close but does not exactly equal \( \frac{40}{57} \), so this option does not satisfy the condition precisely.
4. Rs. 50000: The matching smaller salary would be \( \frac{2}{3} \times 50000 \approx 33333.33 \). Adding Rs. 4000 to each gives 54000 and about 37333.33, and \( \frac{37333.33}{54000} \approx 0.691 \), which does not match \( \frac{40}{57} \) either.

Only Rs. 34000 gives a ratio, after adding Rs. 4000 to each salary, that matches 40:57.

Therefore, the correct answer is Rs. 34000.