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 two salaries start in the ratio 2:3, and after Rs. 4000 is added to each, the ratio becomes 40:57. Since 40:57 simplifies to \( \frac{40}{57} \), we can test each candidate value for the larger salary (Jimmy's) by working backward to the smaller salary and checking whether adding 4000 to both reproduces this exact ratio.

1. Rs. 34000: If the larger original salary is 34000, then since the ratio is 2:3, the smaller salary is \( 34000 \times \frac{2}{3} \approx 22666.67 \). Adding Rs. 4000 to each: \( 26666.67 : 38000 \). Dividing both by \( 666.67 \) gives \( 40 : 57 \), matching the required ratio exactly.
2. Rs. 46800: If the larger salary is 46800, the smaller would be \( 46800 \times \frac{2}{3} = 31200 \). Adding 4000 to each gives \( 35200 : 50800 \), which simplifies to roughly \( 39.6 : 57.2 \), not a clean 40:57 match.
3. Rs. 36700: The smaller salary would be \( 36700 \times \frac{2}{3} \approx 24466.67 \). Adding 4000 gives \( 28466.67 : 40700 \), which does not reduce cleanly to 40:57.
4. Rs. 50000: The smaller salary would be \( 50000 \times \frac{2}{3} \approx 33333.33 \). Adding 4000 gives \( 37333.33 : 54000 \), again not matching 40:57 precisely.

Only Rs. 34000 as the larger salary produces a smaller salary that, after adding Rs. 4000 to both, reduces exactly to the ratio 40:57.

Therefore, the correct answer is Rs. 34000.